Question

Consider a binomial experiment. If the number of trials is increased, what happens to the expected value? To the standard deviation? Explain.

Please give a good and brief explanation (please use a new example that is not on chegg already)

Answer 1

We know in a Binomial Experiment with n number of trails and Probability of Success is p , the expected value will be

E(X) = np

and Standard deviation will be

So, If we assume p is Constant and n will increase , it is expected that both Expected value and Standard deviation will increase. Expected value will increase in direct Proportion whereas Standard deviation will increase to Proportion