StatORJan08 - c. That is, , where c is a positive constant....

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AMS Common Qualifying Examination, Spring Semester 2008 Probability Questions for Statistics and Operations Research 1. Suppose that we have 3 cards identical in form except that both sides of the first card are colored red, both sides of the second card are colored black, and one side of the third card is colored red and the other side black. The 3 cards are mixed up in a hat, and 1 card is randomly selected and put down on the ground. If the upper side of the chosen card is colored red, what is the probability that the other side is colored black?
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Probability Questions for Jan 2008 Let X be a random variable that takes on values between 0 and
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Unformatted text preview: c. That is, , where c is a positive constant. Show that 1 } { = c X P 4 ) var( 2 c X . Probability Questions for Jan 2008 2. Coin A is flipped at times 1,3,5, and coin B is flipped at times 2,4,6, . The probability that the outcome is TAIL is p A for coin A and p B for coin B. Let T be the number of the flip when the first TAIL is observed. Find ET . Probability Questions for Jan 2008 3. Let X and Y be random variables with the joint cumulative distribution function F X,Y (x,y) defined by F X,Y (x,y) = sin x sin y , where x,y /2. Find E[XY]....
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This note was uploaded on 01/31/2011 for the course AMS 507 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.

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StatORJan08 - c. That is, , where c is a positive constant....

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