Purdue Pete loves to have a presence on campus. Often, he is walking around campus. He looks to give and receive high fives from anyone. when he offers a high five, a random Purdue student will high five him back with probability 0.35. [If you are unfamiliar with a "high five" p|ease ask!) a] Purdue Pete sees a student near the Stewart Center and offers a high five. It is not yet known what this particular student will do. Let the random variable count whether or not this student high ves Purdue Pete back. What distribution, parameter(s], and support of this random variable? b) Now, Purdue Pete sees 10 students walking out the new Wilmeth Active Learning Center [WALC]- He offers each of them a high ve. Let H be the number of students who high ve Pete back from these students outside of WALC. What distribution, pa rameterls], and support of this random variable? c) What is the probability that 7 or B of these students outside WALC will high five Pete back? d) What is the expected number of high fives Purdue will receive of the group of 10 students. What is the standard deviation? e] Out of the ten students, it is known that least one student will always high five anyone. What is the probability 3 students high ve Purdue Pete back? f) How many students would Purdue Pete need to offer a high five to in order to be at least 99% sure that at least one student high fives him back