1. (7 points) LeBron James is practicing free throws. Each time, he is successful with probability p E [0, 1], and all attempts are mutually independent. He will stop once he has scored r times. Let X be the random variable corresponding to the number of times he shoots. For example, if he scores for the rth time on his 20th attempt, then X = 20. (a) (3 points) Let 5 represent a success and F represent a failure. We can represent a sequence of throws as a string of 8'5 and F's, called a "throw sequence.\" Fix It 2 1'. How many length-k throw sequences are there with 1' 5'3, ending in an S? (b) (4 points) Find the PMF of X