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Solve the following: (a)A sample of 3 items is chosen at random from a box containing...

Solve the following:

(a)A sample of 3 items is chosen at random from a box containing 20 items of which 4 are
defective. Let X be the number of defective items in the sample. Find E(X), Var (X), and Var (20 − X).

(b) Given n tosses of a fair coin, let X be the number of heads tossed. Find the pmf of X

(c) Show that Var (X) ≥ 0 for any discrete r.v. X. Also, explain why X is constant if and only if
Var (X) = 0. Hint: write Var (X) = E (X − µ)2 = Px (x − µ)^2pX (x), where µ = E (X)

Math   Statistics-And-Probability   
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