# 1. Let X be the number of heads flipped in 4 independent flips of a fair coin. What is var (X)?…

1. Let X be the number of heads flipped in 4 independent flips of a fair coin. What is var (X)?

2. Let Y be the average of two independent rolls of a fair die. What is var (Y)?

3. Let a ∈ R, and let X be a random variable. Prove that E [a · X] = a · E [X].

4. Let a ∈ R, and let X be a random variable. Prove that var (a · X) = a 2 · var (X)

5. Prove that var (X + Y) = var (X) + var (Y) for two independent random variables X and Y.

(Hint: use Exercise 10.127.)

Let X and Y be independent random variables. Prove that E [X · Y] = E [X] · E [Y].

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