The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is:
A) n / p
B) np(1 - p)
C) np
D) np - 1
E) n(1 - p)

Question

Quizplus · Accepted Answer

The expected value of a discrete probability distribution is the sum of the product of each outcome and its probability. For a binomial distribution with n trials, each trial has two possible outcomes (success or failure) with probability p and (1-p), respectively. Thus, the expected value can be calculated as E(X) = (0 x P(X=0)) + (1 x P(X=1)) + (2 x P(X=2)) + ... + (n x P(X=n)). Using the formula for binomial probabilities, we can write this as E(X) = 0((1-p)^n) + 1(np(1-p)^(n-1)) + 2((n choose 2)(p^2)(1-p)^(n-2)) + ... + n((n choose n)(p^n)). Simplifying this expression, we can factor out n from each term and simplify the binomial coefficients to get E(X) = np. Therefore, the correct answer is C) np.

The Expected Value, E(X), of a Binomial Probability Distribution with N