1. Random Variables. The following distribution represents a random variable (X) the number of homeruns hit in a 7 game baseball series and their respective probabilities.

# of homeruns (X) Probability

1 0.21

2 0.24

3 0.38

4 0.08

5 0.06

6 0.03

a. Is this a valid probability distribution? If so, explain why.

b. Find the expected number of homeruns in a 7 game series. Round to two decimal places.

c. Find the standard deviation for the number of homeruns in the 7 game series. Round to two decimal places.

d. What is the probability of having at least 3 homeruns in the 7 games series?