Supposex bin n p and y bin m p are independent andlet Z x y what is the conditional pmfp x Z

Since a binomial experiment consists of n trials, intuition suggests that for X ~ Bin(n, p), E(X) = np, the product of the number of trials and the probability of success on a single trial. V(X) is not so intuitive.

Another way of looking at it From a (more technical) standpoint, two random variables are independent if either of the following statements are true: P(x|y) = P(x), for all values of X and Y.

The Poisson distribution is actually a limiting case of a Binomial distribution when the number of trials, n, gets very large and p, the probability of success, is small. As a rule of thumb, if n≥100 and np≤10, the Poisson distribution (taking λ=np) can provide a very good approximation to the binomial distribution.

Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment). If the probability of success on an individual trial is p , then the binomial probability is nCx⋅px⋅(1−p)n−x .