1. A wheel spun has equal probabilities of 1/3 for the numbers 1, 2 and 3 appeared each. If number 1 appears, the player gets a score of 1.0; if number 2 appears, the player gets a score of 2.0; if number 3 appears, the player gets a score of , where is a normal random variable with mean 3 and standard deviation 1.

a. If represents the player's score on one spin of the wheel and represents the random variable of the wheel spun, then define the respective conditional probabilities, |(|) for =1,2,3.

b. What is (1.5)?

c. Find the expectation and variance of the score.