A hockey player is to take 3 shots on a certain goalie. The probability he will score a goal on his first shot is 0.45. If he scores on his first shot, the chance he will score on his second shot increases by 0.1; if he misses, the chance that he scores on his second shot decreases by 0.1. This pattern continues to on his third shot: If the player scores on his second shot, the probability he will score on his third shot increases by another 0.1; should he not score on his second shot, the probability of scoring on the third shot decreases by another 0.1.

A random variable
counts the number of goals this hockey player scores.

(a) Complete the probability distribution of
below. Use four decimals in each of your entries.

x 0 1 2 3
P (X=x)
(b) How many goals would you expect this hockey player to score? Enter your answer to four decimals.


E(X)

(c) Compute the standard deviation the random variable
. Enter your answer to two decimals.
SD(X)