Every day when she first wakes up Elena takes three foul sho

Every day when she first wakes up, Elena takes three foul shots on a basketball court. For i =1, 2,3 let Yi represent the event “Elena makes shot i.” Suppose (PY1)=(PY2)=(PY3)=.8. Suppose also that “the shots are independent” (i.e., the probability that Elena makes any particular shot does not depend on whether she makes or misses any of the other shots).

Let T! be a random variable defined as the number of shots Elena makes (out of the three she takes).

a) Is T! a member of any family of RVs we have discussed in class? If so, what kind is it?

b) Write down the probability distribution function of T! .

c) Find the expected value of T! .

d) Find the variance of T! .

Solution