EX8 - AMS 410 Actuarial Mathematics Fall 2009 Exercise 8:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exercise 8: Transformation 11/17/2009 1. Transformation. In the following three cases, calculate the probability density function of Y . •X •X •X follows Uniform (-1,1), follows Uniform (-1,1), follows Uniform (0,1), Y = X 2. Y = X 3. Y = X 2. 2. Transformation. An actuary models the lifetime of a device using the random variable Y = 10X 0.8 , where X is an exponential random variable with mean 1 year. Determine the probability density function f (y ), for y > 0, of the random variable Y . 1 3. Max. Claim amounts for wind damage to insured homes are independent random variables with common density function f (x) = where 3x−4 0 for x > 1, otherwise. x is the amount of a claim in thousands. Suppose 3 such claims will be made. What is the expected value of the largest of the three claims? 4. Convolution. Two independent random variables X1 and butions with means of 2 and 3 respectively. What the pdf of X2 follow the exponential Y = X1 + X2 ? distri- 5. Variance. Z are independent random variables following exponential distribuα, β and 4. Given the information: U = X + Y + Z , V = X − Y , E (U ) = V ar(V ), E (U ) − E (V ) = V ar(U )−V ar(V ) . What is α? 2 tions with means of X, Y and 2 ...
View Full Document

Page1 / 2

EX8 - AMS 410 Actuarial Mathematics Fall 2009 Exercise 8:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online