Problem No. 7.1 110 pts. Let discrete random variable X ~ Bin(7, 0.25). Find:
1) Probability P(X > 5)
2) Probability P(X > 2)
3) Probability P(2 < X < 5)
4) Probability P(2 < X < 5)
5) Probability P(X = 0)
6) Probability P(X = 7)
7) E(X)
8) Var(X)
Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
Solution (Show all intermediate steps, formulas, calculations, explanations, and comments below this line. Don't write above this line)