Question

2. Students sometimes delay doing laundry until they finish their problem sets. Assume all random values described below are mutually independent.

(a) A busy student must complete 3 problem sets before doing laundry. Each problem set requires 1 day with probability 2/3 and 2 days with probability 1/3. Let B be the number of days a busy student delays laundry. What is E(B)?

Example: If the first problem set requires 1 day and the second and third problem sets each require 2 days, then the student delays forB = 5 days.

(b) A relaxed student rolls a fair, 6-sided die in the morning. If he rolls a 1, then he does his laundry immediately (with zero days of delay). Otherwise, he delays for one day and repeats the experiment the following morning. Let R be the number of days a relaxed student delays laundry. What is E(R)?

Example: If the student rolls a 2 the first morning, a 5 the second morning, and a 1 the third morning, then he delays for R = 2 days.

(c) Before doing laundry, a nostalgic student must dream of riding the LX bus for a number of days equal to the product of the numbers rolled on two fair, 6-sided dice. Let N be the expected number of days a nostalgic student delays laundry. What is E(N)?

Example: If the rolls are 5 and 3, then the student delays for N = 15 days.

(d) A student is busy with probability 1/2, relaxed with probability 1/3, and nostalgic with probability 1/6. Let D be the number of days the student delays laundry. What is E(D)?

Answer 1