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

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STAT 410 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 ( 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.

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