Show if X is a binomial random variable?

Question

Mue sub x = n p

Answer 1

that is the definition for the expected value of a binomial random variable. the expected value is equal to the number of trials time the probability of one sucesses.

Answer 2

E(x) = np
But the definition of mue is E(x)
Therefore mue = np

Answer 3

Mike is wrong. That's not the definition of expected value.

You can do it yourself:
E(X) is the sum over all possible values of X of the product of x times the pdf(x):

Just sum k=0 to n [k*pdf(n,k)]

It's actually very tricky to do to get a general solution but easy computationally.