Homework #7 STAT 505 Fall 2011

1. In basketball, a player often gets to shoot a one-and-one meaning if the first free throw goes in, he/she gets to shoot another. Assume the two shots are independent, and that different players have different probabilities of making their free throws, p (assumed constant for any individual). You can look at players stats on wnba.com or nba.com to see what personal career averages on FT's are. I see numbers ranging from 0.59 to 0.90.
   1. Build an R function to simulate the process of shooting a one and one. It should take as input the player's probability of making a free throw. Output: 0, 1, or 2 points (successes). Show the function and a table of the output of 100 runs when p = 0.50.
   2. For each integer percentage from 50% to 95%, run your simulation 1000 times and store the scores (0, 1, or 2 pts). Plot the average score against the percentage.
   3. Add "error bands" to encompass plus/minus 1 standard deviation from the mean. These should get truncated at the top (2 is max) and bottom (0 is min). (See functions pmin and pmax).
   4. Use conditional probability to find the expected value of the number of points for a 1-and-1 as a function of p, the probability of success. Add this curve to your plot with a different line type. Include a legend.
2. Exercise 8 p 152-3