This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009
Exercise 6: Other questions 10/20/2009
1. The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. Calculate the probability that the component will work without failing for at least ve hours. 2. An insurance policy is written to cover a loss, X , where X has a uniform distribution on [0, 1000]. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible? 3. The warranty on a machine species that it will be replaced at failure or age 4, whichever 1 for 0 < x < 5 occurs rst. The machines age at failure, X , has density function f (x) = 5 . 0 otherwise Let Y be the age of the machine at the time of replacement. Determine the variance of Y . 4. Three individuals are running a one kilometer race. The completion time for each individual is a random variable. Xi is the completion time, in minutes, for person i. X1 : uniform distribution on the interval [2.9, 3.1] X2 : uniform distribution on the interval [2.7, 3.1] X3 : uniform distribution on the interval [2.9, 3.3] . The three completion times are independent of one another. Find the probability that the earliest completion time is less than 3 minutes. 1 5. The number of a major hurricane in each year follows a Poisson distribution with parameter λ. It is found that it is 1.5 times as likely that a major hurricane will occur in the next ten years as it is that the next major hurricane will occur in the next ve years. Find λ. 6. Suppose X has the pdf f (x) = 2x, 0 < x < 1. Calculate: P (X > 0.5X > 0.4), P (X > 0.4X > 0.5), E (X X > 0.5). 7. Let X be exponentially distributed with mean 2. Determine: P (X > 5X > 2), E (X X > 2), V ar(X X > 2). 2 ...
View
Full
Document
This note was uploaded on 08/08/2010 for the course AMS 410 taught by Professor Yang,y during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Yang,Y

Click to edit the document details