In: Statistics and Probability
3. Suppose each time Illini freshman sensation Ko Cockburn shoots a free throw he has
a chance of making it.
a. Construct a prior distribution for theta to be Beta(a,b). What values should a and b
take so that the prior mean is 0.5 and the prior standard deviation is 0.2?
b. In his first game against Nicholls State Ko made 2 foul shots out of 6 attempts.
What was the posterior distribution for theta after this game?
c. What was the mean of the posterior distribition?
d. What was the standard deviation of the posterior distribution?