Homework 3
1) Problem 8 Page 228 Suppose that 10 trains arrive independently at a station every day, each at random time between 10:00am and 11:00am. What is the expected number and the variance of those that arrive between 10:15am and 10:28am? Solution:
Homework 5
1) Problem 2 Page 365 A fair die is tossed twice. The sum of the outcomes is denoted by X and the largest value by Y. (a) Calculate the joint probability mass function of X and Y; (b) Find the marginal probability mass function of X and Y; (c)
Final Exam
Problem 1 (15 pts.) An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the companys policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Eac
Homework 4
1) Problem 1 Page 258 Let X be a random number from
. Find the probability density function of
.
Solution: Let F be the distribution function of Y. Clearly,
. For
,
So
2) Problem 3 Page 258 Let X be a continuous random variable with density fun