Question

Tradition says that an undergraduate student won’t graduate in four years if he/she walks underneath the Bell Tower at Purdue. Every time an undergraduate student walks past the tower, the probability that the student will walk underneath the tower is 0.08. Assume that each student is independent of any others.

d) 6 students have walked past the bell tower and none of these students walked underneath it. What is the probability that it takes more than 14 students (total) walking past the bell tower until the first student walks underneath it? State the distribution and parameter(s) you are using.

*** question from Chegg user: Is this a geometric distribution D~Geometric(p=0.08)? If so, can I use tail property and memoryless property here, P(D>14| D>8) = P(D>8) using memoryless and then tail property = (1-.08)^(8) = .5132 as the answer?***

e) What is the probability that the 10th student walking past the bell tower is the 2nd student to walk underneath the tower? Also state the distribution and parameter(s) that you are using.

*** Is this Binomial or Negative Binomial? ***

f) Find the expected value and standard deviation of the number of students who walk past the bell tower until the second one to walk underneath it.

Answer 1