410Hw03 - STAT 410 Summer 2009 Homework #3 (due Monday,...

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

View Full Document Right Arrow Icon
Summer 2009 Homework #3 (due Monday, June 29, by 4:00 p.m.) 1. Suppose Heidi has a fair 4-sided die, and Alex has a fair 6-sided die. Each day, they roll their dice (independently) until someone rolls a “1”. (Then the person who did not roll a “1” does the dishes.) Find the probability that … a) they roll the first “1” at the same time (after equal number of attempts); b) it takes Alex twice as many attempts as it does Heidi to roll the first “1”; c) Alex rolls the first “1” before Heidi does; d) Alex rolls the first “1” on an even-numbered attempt; e) Alex rolls a “1” before he rolls an even number. 2. Let X, Y, and Z be i.i.d. Uniform [ 0 , 1 ] random variables Find the probability distribution of W = X + Y + Z. That is, find ( 29 w f W . Hint: If V = X + Y, we know the p.d.f. of V, f V ( v ) ( see Examples for 06/24/2009 ): f V ( v ) = v if 0 < v < 1, f V ( v ) = 2 – v if 1 < v < 2, f V ( v ) = 0 otherwise. Now use convolution formula to find the p.d.f. of W = V + Z. There will be 5 possible cases;
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

410Hw03 - STAT 410 Summer 2009 Homework #3 (due Monday,...

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