Practice - Problem 3 If X,X n are independent with means μ...

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OR 3500/5500, Summer’08 Practice Problems Not to be turned in. Problem 1 You have a fair coin and you keep tossing it until you get 5 heads. (a) Find the probability that you will need to toss the coin exactly 20 times. (b) If X is the random variable which denotes the number of times you need to toss the coin to get k heads, find the probability mass function of X . Problem 2 Find the probability that a poker hand of 5 cards will contain no card smaller than 7, given that it contains at least 1 card over 10(Ace is the highest card).
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Unformatted text preview: Problem 3 If X , ...,X n are independent with means μ and variance σ 2 , then find E h n X i =1 ( X i-¯ X n ) 2 i . Problem 4 If X ∼ Gamma ( α,λ ). Find E ( X k ) ,k ≥ 1 . Problem 5 If X and Y are independent N (0 , 1), show that P [ X 2 + Y 2 ≥ 8] ≤ 1 8 . (Given: E ( X 4 ) = 3) Problem 6 Boxes and balls again!!! Suppose n balls are thrown randomly into n boxes. Find the probability that only box 1 is empty. 1...
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