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Mathematical Statistics Quiz#1--2008

# Mathematical Statistics Quiz#1--2008 - Quiz#1 6:309:00PM...

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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|A ת Bሻ ൌ PሺC|Bሻ , then PሺA|B ת Cሻ ൌ PሺA|Bሻ . (2) PሺA ת Bሻ ൒ PሺAሻ ൅ PሺBሻ െ 1 . 3. Consider the trivariate probability density fሺx , x , x ሻ ൌ ቄ ሺx ൅x ሻe ି୶ , for 0 ൏ x ൏ 1, 0 ൏ x ൏ 1, 0 ൏ x 0 otherwise , (1) Find the marginal density of X and X

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Mathematical Statistics Quiz#1--2008 - Quiz#1 6:309:00PM...

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