Show that E(X) = np when X is a binomial random variable.

Chapter 4, Problem 64E

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QUESTION:

Show that E(X) = np when X is a binomial random variable. [Hint: First express E(X) as a sum with lower limit x = 1.Then factor out np, let y = x - 1 so that the sum is from y = 0 to y = n - 1, and show that the sum equals 1.]

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QUESTION:

Show that E(X) = np when X is a binomial random variable. [Hint: First express E(X) as a sum with lower limit x = 1.Then factor out np, let y = x - 1 so that the sum is from y = 0 to y = n - 1, and show that the sum equals 1.]

ANSWER:

Problem 64E Answer: Step1: Let “X” be random variable it follows binomial distribution with parameters “p” and “n”. The probability mass function of binomial distribution is given by p(x) = C p q n-, x = 0,1,2,...,n x We need to p

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