Let U be a discrete random variable taking the values a1,...,ar with probabilities p 1 ,...,pr. a. Suppose all ai ≥ 0, but that E[U]=0. Show then In other words; P(U = 0) = 1 b. Suppose that V is a...

Let U be a discrete random variable taking the values a1,...,ar with probabilities p₁,...,pr.

a. Suppose all ai ≥ 0, but that E[U]=0. Show then

In other words; P(U = 0) = 1

b. Suppose that V is a random variable taking the values b1,...,br with probabilities p₁,...,pr. Show that Var(V ) = 0 implies

P(V = E[V ]) = 1.