problemset36 - X,Y in question#3 of Problem Set 35 in which...

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STAT/MA 416 November 30, 2011 Problem Set 36 Name: 1. Consider a tray with 8 lemonades and 3 raspberry juices. Alice and Bob each take 1 drink from the tray, without replacement. Assume that all of their choices are equally likely. Let X be the number of lemonades that Alice and Bob get. (Note: X is either 0, 1, or 2.) Find the variance of X . 1
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2. In question #1, let X 1 and X 2 indicate (respectively) if Alice and Bob (respectively) get lemonade. In other words, X 1 = 1 if Alice gets lemonade, or X 1 = 0 otherwise; and X 2 = 1 if Bob gets lemonade, or X 2 = 0 otherwise. Find the correlation ρ ( X 1 , X 2 ) between X 1 and X 2 . 2
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3a. For the X, Y in question #1 of Problem Set 35, in which Jim cuts wood, and Y = 2 X +2, find Cov( X, Y ), i.e., the covariance of X and Y . b. Find the correlation ρ ( X, Y ) of X and Y . 3
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4a. For the
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Unformatted text preview: X,Y in question #3 of Problem Set 35, in which Y = ( X-1)( X +1) = X 2-1, find Cov( X,Y ), i.e., the covariance of X and Y . b. Find the correlation ρ ( X,Y ) of X and Y . 4 5. Roll two 4-sided dice ( not 6-sided dice ). Let X be the minimum value, and let Y be the maximum value. Find the covariance of X and Y . 5 6. Design your own problem and solution. Create your own problem about the correlation of two discrete or continuous random variables. Design your problem in such a way that you would find it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
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