In probability theory and statistics, the hypergeometric distribution is a discr
ID: 3226232 • Letter: I
Question
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K successes, wherein each draw is either a success or a failure. Let X be a hypergeometric distribution (with n draws, n Z+ arbitrary positive integer), find P (X = k). Compare hypergeometric distribution and binomial distribution - what does binomial distribution describe compared to hypergeometric distribution.
Explanation / Answer
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K successes, wherein each draw is either a success or a failure. Let X be a hypergeometric distribution :
Then P(X=k) = (K C k)* ((N-K) C (n-k)) / (N C n)
Compare hypergeometric distribution and binomial distribution - what does binomial distribution describe compared to hypergeometric distribution.
All of these distributions are counts when you're sampling.
They represent number of successes in your fixed number of draws (Binomial and Hypergeometric). For the Hypergeometric and Negative Hypergeometric distributions, you're assuming that there's a fixed number of successes and failures in the population and the probability of drawing a "success" change as you remove items from the population.
Assumptions of Binomial and Hypergeometric distribution :
Hypergeometric distribution :