Suppose a friend has thought of a value between 1 and 100 and would like you to guess the value that was chosen. a. If you have an equally likely chance of selecting ANY value from this range, what is the expected value of the possible value your friend has chosen? b. What is the standard deviation of the possible chosen values? c. What is the probability that the value you guess would be within 20 units of your friends chosen value? d. Show, using the manual definition for variance, that for ANY continuous uniform distribution the variance is of the form 2 = (b-a) 2 12