Mean of a binomial distribution. May 31, 2019 · The function BINOM.
x = total number of successes. 0000 0. The variance of the binomial distribution is the spread of the probability distributions with respect to the mean of the distribution. The binomial distribution is related to sequences of fixed number of independent and identically distributed Bernoulli trials. To find the mean, use the formula $$ \mu = n \cdot p $$ where n is the number of trials and p is the probability of success on a single trial. 5 for a coin toss). ℓ ( π) = f ( x 1, …, x n; π) = π ∑ i x i ( 1 − π) n − ∑ i x i. The probability of success on any one trial is the same number Courses on Khan Academy are always 100% free. The syntax for the instructions are as follows: To calculate (x = value): binompdf(n, p, number) if "number" is left out, the result is the binomial probability table. The characteristic function for the binomial distribution is. n is the number of trials. If n is very large, it may be treated as a continuous Nice question! The plan is to use the definition of expected value, use the formula for the binomial distribution, and set up to use the binomial theorem in algebra in the final step. 06. The binomial probability is a discrete probability distribution, with appears frequently in applications, that can take integer values on a range of [0, n] [0,n], for a sample size of n n. Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0, and so we can actually write: E [ X ] = Σ x = 1n x C (n , x) p x (1 – p) n – x . 5 ). For a Binomial distribution, μ μ, the expected number of successes, σ2 σ 2, the variance, and σ σ, the standard deviation for the number of success are given by the formulas: μ = np σ2 = npq σ = npq−−−√ μ = n p σ 2 = n p q σ = n p q. ∴ npq<np. For example: if you tossed a coin 10 times to see how many heads come up, your probability is . I'll leave you there for this video. To derive formulas for the mean and variance of a binomial random variable. The number 0. Over all 100 runs, compute the square root of the average of the squares of the errors, when \ (M\) used to estimate \ (p\). Mean of Binomial Distribution formula is defined as the long-run arithmetic average of individual values of the random variable that follows Binomial distribution and is represented as μ = N Trials *p or Mean in Normal Distribution = Number of Trials*Probability of Success. P^r. The reason that the number of samples matters is because you are dealing with a small sample of the population. People in Mathematics. I understand that the first and second central moments are mean and variance respective First, use the sliders (or the plus signs +) to set \ (n=5\) and \ (p=0. q^n\) A binomial experiment is an experiment consisting of a fixed number of independent Bernoulli trials. 35). Number of trials. Think of trials as repetitions of an experiment. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. 3333 0. E. (In this case, 21. The mean, μ μ, and variance, σ2 σ 2, for the binomial probability distribution are μ = np μ = n p and σ2 = npq σ 2 = n p q. Click the Calculate button to compute binomial and cumulative probabilities. results from each trial are independent from each other. ”. 5 (i. 5 from x x (use x + 0. The normal distribution as opposed to a binomial distribution is a continuous distribution. Davis is doing an activity with her statistics students where she gives them a 20 -question multiple choice test, and they know none of the answers. trials: total number of trials. Compute the pdf of the binomial distribution counting the number of successes in 50 trials with the probability 0. We must first introduce some notation which is necessary for the binomial which is the normal distribution with parameters µ = np and σ2 = npq, up to corrections that vanish as n → ∞. model alpha beta mean mode var sd 1 prior 1 2 0. 5 x + 0. 二項式分布. Then, as you move the sample size slider to the right in order to increase \ (n\), notice that the distribution moves from being skewed to the right to approaching symmetry. The distribution defined by the density function in (1) is known as the negative binomial distribution; it has two parameters, the stopping parameter k and the success probability p. The negative binomial distribution has a variance /, with the distribution becoming identical to Poisson in the limit for a given mean (i. the probability of failure is 1-p. Jul 13, 2024 · The binomial distribution is implemented in the Wolfram Language as BinomialDistribution [ n , p ]. 1 is a discrete probability distribution: It shows the probability for each of the values on the X -axis. May 22, 2015 · If for a binomial distribution the mean is $4$ and variance is $3$, find th $3^{\\text{rd}}$ central moment. Certain types of probability distributions are used in hypothesis testing, including the standard normal distribution, the F distribution, and Student’s t distribution. It gives us an idea of how dispersed the outcomes are from the expected number of successes. This distribution occurs when there are events that do not occur as the outcomes of a definite number of outcomes. The mean of the binomial distribution B ( n, p) is np. In the binomial coin experiment, select the number of heads \ (Y\), and set \ (p = 0. Mar 26, 2023 · Definition: binomial distribution. We want the probability of obtaining two sixes so we are concerned with P[X = 2] P [ X = 2]. The binomial distribution represents the probability for 'x' successes of an experiment in 'n' trials, given a success probability 'p' for each trial at the experiment. The random variable X X = the number of successes obtained in the n n independent trials. When looking at a person’s eye color, it turns out that 1% of people in the world has green eyes ("What percentage of," 2013). D. where μ is the mean of the binomial distribution. It is used when there are only two possible outcomes, like heads or tails, and the probability of success is the same for each trial. It is an exact probability distribution for any number of discrete trials. (In this case, heads. 5). 2. To calculate the standard deviation for a given binomial distribution, simply fill in the values below and then click the “Calculate” button. When N is large, the binomial distribution with parameters N and p can be approximated by the normal distribution with mean N*p and variance N*p*(1–p) provided that p is not too large or too small. For Maximum Variance: p=q=0. 9% chance that I will roll 4 or fewer skulls. We have E(e^(tx)) = sum over all possible k of P(X=k)e^(tk) = sum k from 0 to n of p^k (1-p)^(n-k) (n choose k) e^(tk) Jun 4, 2024 · What is Binomial Distribution Mean and Variance? Binomial Distribution Mean tells about the average success obtained in ‘n’ number of trials. The binomial distribution describes the probability of having exactly k successes in n independent Bernoulli trials with probability of a success p (in Example \(\PageIndex{1}\), n = 4, k = 1, p = 0. , in a set of patients) and the outcome for a given patient is either a success or a failure. In other words, it is the probability distribution of the Binomial Distribution Function. Jan 29, 2021 · σ = √np (1-p) It turns out that if n is sufficiently large then we can actually use the normal distribution to approximate the probabilities related to the binomial distribution. where: n = number of trials. 掷硬币 十次出现五次正面的概率、产品合格率 时抽出一百件 Aug 24, 2021 · Go into 2 nd DISTR. Binomial Distribution in Statistics: The binomial distribution forms the base for the Solution: The mean of the binomial distribution is interpreted as the mean number of successes for the distribution. When calculating the Likelihood function of a Binomial experiment, you can begin from 1) Bernoulli distribution (i. The probability of obtaining more successes than the observed in a binomial distribution is. 5, the distribution is symmetric about the mean. What happens if there aren't two, but rather three, possible outcomes? Since a binomial random variable is a discrete random variable, the formulas for its mean, variance, and standard deviation given in the previous section apply to it, as we just saw in Note 4. Jan 29, 2019 · We begin by using the formula: E [ X ] = Σ x=0n x C (n, x)px(1-p)n – x . See examples, formulas, graphs and bias effects. n — The number of trials. Students need to guess on every question, and each question has 5 possible choices, 1 of which is correct. Suppose that the experiment is repeated several times and the repetitions are independent of each other. This number is a measure of the quality of the estimate. The integral of the rest of the function is square root of 2xpi. The discrete random variable follows a binomial distribution if it counts the number of successes when an experiment satisfies the conditions: There are a fixed finite number of trials. DIST finds the probability of getting a certain number of successes in a certain number of trials where the probability of success on each trial is fixed. You n Apr 23, 2022 · 1/4. 1 λ. 23570 2 posterior 100 3 0. The standard deviation for the binomial distribution is defined as: σ = √ n*p* (1−p) where n is the sample size and p is the population proportion. Their answers are correct in theory but they need approximation using normal distribution since the distribution of test statistic does not exactly follow Normal May 19, 2020 · Mean of binomial distributions proof. Therefore, this is an example of a binomial distribution. 7687492. State the random variable. The random variable, X, counts the number of trials required to obtain that first success. The variance of a Binomial Variable is always less than its mean. May 22, 2016 · I was reading Introduction to Probability Models 11th Edition and saw this proof of why Poisson Distribution is the approximation of Binomial Distribution when n is large and p is small: An import If you take a sample of the binomial distribution the mean of that sample will not (often) be 42 * 0. Random number distribution that produces integers according to a binomial discrete distribution, which is described by the following probability mass function: This distribution produces random integers in the range [0,t], where each value represents the number of successes in a sequence of t trials (each with a probability of success equal to p). Binomial Distribution Variance is the measurement of Apr 21, 2020 · The binomial distribution table is a table that shows probabilities associated with the binomial distribution. Sample size n Jun 24, 2018 · Pr[Y = y] = p(1 − p)y, y = 0, 1, 2, …. It is easy to verify that E(Bi) = p, so E(X) = np. . For n = 6, the low is 2. The scenario outlined in Example \(\PageIndex{1}\) is a special case of what is called the binomial distribution. In a suitable controlled trial, with independent events and constant probabilities, the best estimates for the population mean and variance are the sample mean and variance. S – successes (probability of success) are the same – yes, the likelihood of getting a Jack is 4 out of 52 each time you turn over a card. Divide the numbers you found in the table by the number of population members. A Poisson random variable “x” defines the number of successes in the experiment. Indeed, the mean value µ and the standard deviation σ of the normal approximation are identical to the mean value and the standard deviation of the original binomial distribution, respectively. For a binomial distribution having n trails, and having the probability of success as p, and the probability of failure as q, the mean of the binomial distribution is μ = np, and the variance of the binomial distribution is σ 2 =npq. May 1, 2015 · In a Binomial experiment, we are interested in the number of successes: not a single sequence. Nov 1, 2012 · But then by the linearity of expectation, we have E(X) = E(B1 + B2 + ⋯ + Bn) = E(B1) + E(B2) + ⋯ + E(Bn). If you try to graph that, you'll see Enter a value in each of the first three text boxes (the unshaded boxes). 7. single trial) or 2) just use Binomial distribution (number of successes) 1) Likelihood derived from Bernoulli trial Oct 21, 2020 · Then the binomial can be approximated by the normal distribution with mean μ = np μ = n p and standard deviation σ = npq−−−√ σ = n p q. If there are 50 trials, the expected value of the number of heads is 25 (50 x 0. ‘q’ is the probability of failure, q = 1 - p. 5. 1 shows the probability of 0, 1, and 2 successes for two trials (flips) for an event that has a probability of 0. Because we have n = 3 n = 3 trials and a probability of success p = 1 6 p = 1 6, X ∼ Bin(n,p) X ∼ B i n ( n, p) or, more specifically, X ∼ Bin(3, 1 6) X ∼ B i n ( 3 For the binomial distribution, the variance, mean, and standard deviation of a given number of successes are expressed by the following formula $$ Variance, σ2 = npq $$ $$ Mean, μ = np $$ $$ Standard Deviation σ= √(npq) $$ These formulae are used by a binomial distribution calculator for determining the variance, mean, and standard deviation. 4. Also, the population variance is computed as: \sigma^2 = n\cdot p \cdot (1-p) σ2 = n⋅ p⋅ The likelihood function is the joint distribution of these sample values, which we can write by independence. 5 x − 0. Take it to the extreme to see how this would work. So, we can treat the actual World Series as a binomial experiment with seven trials. In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. Dan and Abaumann's answers suggest testing under a binomial model where the null hypothesis is a unified single binomial model with its mean estimated from the empirical data. DIST(number_s, trials, probability_s_cumulative) number_s: number of successes. You might recall that the binomial distribution describes the behavior of a discrete random variable X, where X is the number of successes in n tries when each try results in one of only two possible outcomes. Defining a head as a "success," Figure 5. Mean, μ = np. Khan Academy is a nonprofit with the mission of providing Geometric Distribution Binomial Distribution; A geometric distribution is concerned with the first success only. variance: \( σ 2 = npq \) standard deviation \( σ = \sqrt{npq} \) Range rule of thumb: Values not significant: Between (μ - 2σ ) and (μ + 2σ ) Find parameters of binomial distribution. Start practicing—and saving your progress—now: https://www. May 21, 2019 · Binomial Standard Deviation Calculator. 5\) and \ (n = 15\). The variance of the binomial distribution is: σ 2 = Nπ (1-π) where σ 2 is the variance of the binomial distribution. Poisson binomial distribution. Both of these functions can be accessed on a TI-84 calculator by pressing 2nd and then pressing vars. Formula for Mean of Binomial Distribution. Notice that the binomial distribution is skewed to the right. The formulas below are used to indicate the mean, variance, and standard deviation for a binomial distribution for a certain number of successes. Tails. This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression . Jan 17, 2022 · This video goes over the mean of the Binomial Distribution, the expected value of the Binomial distribution, the variance of the Binomial Distribution and th Feb 8, 2021 · To find the mean (sometimes called the “expected value”) of any probability distribution, we can use the following formula: Mean (Or "Expected Value") of a Probability Distribution: μ = Σx * P(x) where: •x: Data value. khanacademy. So it must be normalized (integral of negative to positive infinity must be equal to 1 in order to define a probability density distribution). ) k — The number of successes. So, for example, using a binomial distribution, we can determine the probability of getting 4 heads in 10 coin tosses. In other words, the values of the variable vary based on the underlying probability distribution. 6 in a single trial . The distribution of the number of experiments in which the outcome turns out to be a success is called binomial distribution. Suppose a random experiment has the following characteristics. To calculate P(x ≤ value): binomcdf(n, p, number) if "number" is left out, the result is the cumulative binomial probability table. If W is the number of games won by the Reds, the probability that the Reds win the World Series is P(W ≥ 4). The y-axis contains the probability of x, where X = the number of workers who have only a high school diploma. The expected mean of the Bernoulli distribution is denoted as E[X] = p. Typically, analysts display probability distributions in graphs and tables. To understand the steps involved in each of May 19, 2020 · Jacob Bernoulli. May 31, 2019 · The function BINOM. Figure 5. By manipulating the factorials involved in the expression for C (n, x) we Apr 23, 2022 · The probability distribution of Vk is given by P(Vk = n) = (n − 1 k − 1)pk(1 − p)n − k, n ∈ {k, k + 1, k + 2, …} Proof. 5 or x − 0. “Independent” means that the result of any trial (for example, trial one) does not affect the results of the following trials, and all trials are conducted under the same conditions. Here, X is the random variable. There are a fixed number of trials. Binomial Probability Distribution a discrete random variable (RV) that arises from Bernoulli trials; there are a fixed number, \(n\), of independent trials. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. e. Mean and Variance of a Binomial Distribution. The outcome of each trial is independent of the outcomes of the other trials. To find the mean (μ) and the associated confidence interval: Locate the 95% low and high values in the table for 95% exact confidence intervals for the Poisson Distribution. There are only two possible outcomes, called “success” and “failure,” for each trial. Variance, σ2 = n × p × q. The binomial distribution function specifies the number of times (x) that an event occurs in n independent trials where p is the probability of the event occurring in a single trial. Number of Trials is the total number of repetitions of a particular For normalization purposes. Write the probability Jan 20, 2017 · شرح الـBinomial distribution باللغة العربية مع أمثلة . Remember that q = 1 − p q = 1 − p. That is, for φ(x) = 1 √ 2πnpq Apr 23, 2018 · A probability distribution is a statistical function that describes the likelihood of obtaining all possible values that a random variable can take. The letter n. , mX(u) =(mY(u))r. 202 and the high is 13. Consider an experiment having two possible outcomes: either success or failure. 5 is called the Example: The probability of getting a head i. The concept is named after Siméon Denis Poisson . The probability of “failure” is 1 – P (1 minus the probability of success, which also equals 0. when the failures are increasingly rare). 0555556 0. Here's a summary of our general strategy for binomial probability: P ( # of successes getting exactly some) = ( arrangements # of) ⋅ ( of success probability) ( successes # of) ⋅ ( of failure probability) ( failures # of) Using the example from Problem 1: n = 3. The probability of failure is often denoted by q. There are only two possible outcomes, called “success” and “failure,” for 17. (4) is the beta function, and is the incomplete beta function . Now if you already know that the MGF of the geometric distribution is. In order to get the best approximation, add 0. The standard deviation, σ σ, is then \sigma The Bernoulli distribution is a special case of the binomial distribution with = [4] The kurtosis goes to infinity for high and low values of p , {\displaystyle p,} but for p = 1 / 2 {\displaystyle p=1/2} the two-point distributions including the Bernoulli distribution have a lower excess kurtosis , namely −2, than any other probability Aug 10, 2020 · The Binomial Distribution. May 4, 2023 · The mean of a binomial distribution is: \(\text{Mean denoted by }\mu=np;\text{ where n is the number of observations and p is the probability of success}\) For the instant when p = 0. Explore math with our beautiful, free online graphing calculator. 29 "Example 7" in the case of the mean. This will take you to a DISTR screen where you can May 3, 2023 · We will do this by using the binomial distribution: It means the following: P (X = k) — The probability of obtaining k successful outcomes in a total of n independent trials. The value of a binomial is obtained by multiplying the number of independent trials by the successes. So the above argument shows that the combinatorial identity of your problem is correct. In the negative binomial Mar 13, 2024 · The outcomes of a binomial experiment fit a binomial probability distribution. DIST is as follows: BINOM. This Statistics video tutorial explains how to find the probability of a binomial distribution as well as calculating the mean and standard deviation. May 28, 2023 · They are derived from the general formulas. The syntax for BINOM. Binomial Distribution Mean is also called Binomial Distribution Expectation. g. 76. 41). 1 : The graph of X ∼ B(20, 0. Consider a group of 20 people. In the next video we'll graphically represent this and we'll see the probability distribution for this random variable. The binomial distribution is used in statistics as a building block for Apr 13, 2020 · binomcdf (n, p, x) returns the cumulative probability associated with the binomial cdf. Solved Example for You Learn how to calculate the probability of getting a specific number of successes in a series of trials with two possible outcomes. In practical terms, it helps in understanding the reliability or predictability of the outcomes. 5 of being a success on each trial. In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. Exercise 3. The Bernoulli distribution variance for random variable is expressed as, Var[X] = p (1 – p). you have a 50 percent chance of getting a heads and 50 A binomial distribution is a discrete probability distribution. The population mean is computed as: \mu = n \cdot p μ = n⋅p. p. (3) where. There are \ (n\) identical and independent trials of a common procedure. 在 概率论 和 统计学 中， 二项分布 （英語： binomial distribution ）是一种 离散 概率分布 ，描述在进行 独立 随机试验 时，每次试验都有相同 概率 “成功”的情况下，获得成功的总次数。. In a binomial distribution, there are a fixed number of trials and the random variable, X, counts the number of successes in those trials. It is a special case of the binomial distribution for n = 1. The formula for the mean of binomial distribution is: μ = n *p. However, for the binomial random variable there are much simpler formulas. Example \(\PageIndex{1}\) Finding the Probability Distribution, Mean, Variance, and Standard Deviation of a Binomial Distribution. We start by plugging in the binomial PMF into the general formula for the mean of a discrete probability distribution: Then we use and to rewrite it as: Finally, we use the variable substitutions m = n – 1 and j = k – 1 and simplify: Q. Where p is the probability of success and The notation B (n, p) is used to denote a binomial distribution. •P(x): Probability of value. This is known as the normal approximation to the binomial. Instead, "On Average" the mean of the samples will be 42 * 0. Parameters of binomial distribution: mean μ = np. You wrote down another expression for the mean. For example, consider our probability distribution for the soccer team: Apr 26, 2023 · The binomial distribution is a probability distribution that can be used to describe the number of successful or unsuccessful outcomes in a series of events, which must be independent of each other. They are: Sep 25, 2020 · N – number of trials fixed in advance – yes, we are told to repeat the process five times. Standard Deviation, σ = √ (n × p × q) Where, p is known as the probability of achieving success. n (1-p) ≥ 5. We interpret ℓ ( π) as the probability of observing X 1, …, X n as a function of π, and the maximum likelihood estimate (MLE) of π is the value of π Jul 24, 2016 · The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times (e. Common probability distributions include the binomial distribution, Poisson distribution, and uniform distribution. 01649 Apr 24, 2022 · Run the experiment 100 times. Apr 29, 2024 · The probability distribution remains constant at each successive Bernoulli trial, independent of one another. Mean and standard deviation of a binomial random variable. For example, the number of “heads” in a sequence of 5 flips of the same coin In a binomial distribution the probabilities of interest are those of receiving a certain number of successes, r, in n independent trials each having only two possible outcomes and the same probability, p, of success. Note. With the help of the second formula, you can calculate the binomial distribution. mY(u) = p 1 − (1 − p)eu, the result immediately follows. For example, when tossing a coin, the probability of obtaining a head is 0. Jun 9, 2022 · Heads. Using the techniques from the last example, we get P(Reds win the series) = 0. Probability of success on a trial. Jun 26, 2024 · Binomial Distribution: The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters Recognize the binomial probability distribution and apply it appropriately. 5 to x x or subtract 0. The letter n denotes the number of trials. Ms. e a success while flipping a coin is 0. p = probability of success on a given trial. [1] Let X X be the discrete random variable denoting the number of sixes obtained. 9709 0. 3 - The Trinomial Distribution. The formula for Binomial Distribution Expectation is given as μ = n. Apr 27, 2023 · Here’s the command: pbinom( q= 4, size = 20, prob = 1/6) ## [1] 0. 5 and σ max = n/4. Where “n” is the number of trials and “p” is the probability of success. The beta-binomial distribution is the binomial . In other words, there is a 76. Use Statdisk /Analysis/ Probability Distribution/ Binomial distribution, enter n, p, x, evaluate. Or, to put it another way, R is telling us that a value of 4 is actually the 76. 9th percentile of this binomial distribution. 2\). 0002719 0. Poisson distribution is used under certain conditions. . The Binomial Setting. p is the probability of success. Number of successes (x) Binomial probability: P (X=x) Cumulative probability: P (X<x) Negative Binomial Distribution: f (x) = \ (^ {n + r - 1}C_ {r - 1}. 15 (Summarizing the Beta-Binomial: Take II) Write the corresponding input code for the summarize_beta_binomial() output below. Mean(µ) = np Variance(σ 2) = npq. To understand the effect on the parameters n and p on the shape of a binomial distribution. 8002. To use the binomial distribution table, you only need three values: n: the number of trials; r: the number of “successes” during n trials; p: the probability of success on a given trial Then the Binomial probability distribution function (pdf) is defined as: This distribution has mean, μ = np and variance, σ 2 = npq so the standard deviation σ =√(npq). For n to be “sufficiently large” it needs to meet the following criteria: np ≥ 5. The number of adult workers that you expect to have a high school diploma but not pursue any further education is the mean, μ = np = (20)(0. 41) = 8. where q = 1- p. Also recall that the MGF of the sum of r iid random variables is simply the MGF of one such random variable raised to the rth power; i. 9802 0. More specifically, it’s about random variables representing the number of “success” trials in such sequences. ) p — The chance that a trial is successful. Three characteristics of a binomial experiment. Actually, the normal distribution is based on the function exp (-x²/2). Because there are only two possible outcomes. Each Bernoulli trial is an independent trial and has two possible outcomes, occurrence or non-occurrence (success or failure), and each trial has the same probability In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. To learn how to determine binomial probabilities using a standard cumulative binomial probability table when p is greater than 0. Poisson distribution is a limiting process of the binomial distribution. There are exactly two possible outcomes for each trial, one termed “success” and the other “failure. There are three characteristics of a binomial experiment. org/math/ap-statistics/random-variables The variance of a binomial variable describes the spread or variability of the distribution around the mean (expected value). The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. . You can think of it as a mean proof of a In general, the mean of a binomial distribution with parameters N (the number of trials) and π (the probability of success on each trial) is: μ = Nπ. yy oi za mv yj ki az kb hv rk
