Mathematical Statistics Quiz#1--2008

Mathematical Statistics Quiz#1--2008 -...

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Mathematical Statistics Quiz #1 4/10/2008 6:30 9:00PM 1. (1) Suppose that we have r boxes. Balls are placed at random one at a time into the boxes until, for the first time, some box has two balls. Find the probability that this occurs with the nth ball. (2) Consider the problem of matching n objects, and let i and r denote distinct specified positions. (i) What is the probability that a match occurs at position i and no match occurs at position r ? (ii) Given that there is no match at position r what is the probability of a match in position i ? 2. Prove the following statements. (1) If A, B, and C are three events such that PሺA ת B ת Cሻ ് 0 and PሺC|AתBሻൌPሺC|Bሻ , then PሺA|BתCሻൌPሺA|Bሻ . (2) PሺAתBሻ൒PሺAሻ൅PሺBሻെ1 . 3. Consider the trivariate probability density fሺx ,x ,x ሻൌቄ ሺx ൅x ሻe ି୶ , for 0 ൏ x ൏1 ,0൏x ൏1 ,0൏x 0 otherwise ,
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This note was uploaded on 05/09/2011 for the course DIF 1486 taught by Professor Yow-jenjou during the Spring '11 term at National Chiao Tung University.

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Mathematical Statistics Quiz#1--2008 -...

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