Consider two binomial distributions with n trials each The f

Consider two binomial distributions, with n trials each. The first distribution has a higher probability of success on each trial than the second. How does the expected value of the first distribution compare to that of the second?

Solution

first distribution : Bin(n , p1)

second distribution : Bin(n , p2)

and p1 > p2

We know that the expected value of Bin(n,p) is np, therefore:

expected value of first distribution = np1

expected value of second distribution = np2

p1 > p2 -> np1 > np2 -> expected value of the first distribution is larger.