Question

2. You will spin a roulette wheel an then choose a number from a continuous distribution depending on the outcome: if it comes up red (the wheel has 18 red spaces and 20 others) then choose from fA(a) = (3/2)a^2 for −1 ≤ a ≤ 1; else from fB(b) = 2/15 (b + 2) for −1 ≤ b ≤ 2. Let Y= the number you choose + 1 if red, and + 0 else. a) (5 pts) Find P(Y>1). b) (5 pts) Find P(red |Y>1). c) (5 pts) Find E(Y).

3. For the probability density function f(x) = c|x 2 − 1| for −3 ≤ x ≤ 4 a) (5 pts) find c. b) (5 pts) find P(X2 > 1). c) (5 pts) find P(X > 1|X < 2). d) (5 pts) find FX(x).

Answer 1