I kindly request you to explain it. And, whatever formula you use please mention it. I am struggling in this subject.

A sportscaster examined the number of penalties (X) called against a high school football team in each game. Use the results below to answer each question.

penalties(x) 2 3 4 5 6

Pr(X = x) 0.2 0.1 0.2 0.3 ?

A. To be a valid pmf, the probability of having 6 penalties is........ .

B. Calculate the mean number of penalties, E(X) = .....

C. Calculate the variance, VAR(X) =.... .

D. Calculate the standard deviation, SD(X) = ....

E. Let F(x) be the cumulative distribution function. Calculate F(3.5).