What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? Choose the correct forumla below.

A. Upper E (Upper X )equalsStartRoot np (1 minus p )EndRoot

B. Upper E (Upper X )equalsp Superscript n

C. Upper E (Upper X )equals (1 minus p )Superscript n(1 minus p )Superscript n

D. Upper E (Upper X )equalsnp

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success p,

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

Now,

Substituting,

Factoring out the n and one p from the above expression:

Representing k=x-1 in the above gives us:

This can then be written by the Binomial Formula as: