problemset37

problemset37 - b Find E X 1 | X 2 = 0 4 5 Sally and David...

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STAT/MA 416 December 2, 2011 Problem Set 37 Name: 1. Let X and Y have a joint uniform distribution on the triangle with corners at (0 , 2), (2 , 0), and the origin. Find E ( Y | X = 1 / 2). 1

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2. Roll two 6-sided dice. Let X denote the minimum value that appears, and let Y denote the maximum value that appears. a. Find E ( Y | X = 3). b. Find E ( X + Y | X = 3). [Hint: Using (a)’s answer, you can solve (b) in one line!] 2
3. Let X 1 and X 2 be independent exponential random variables, each with mean 1. Let Y = X 1 + X 2 . Find E ( X 1 | Y = 3). 3

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4. 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 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. a. Find E ( X 1 | X 2 = 1).

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Unformatted text preview: b. Find E ( X 1 | X 2 = 0). 4 5. Sally and David each pick 10 ﬂowers from the case without paying attention to what type of ﬂowers they are picking. There are a large quantity of ﬂowers available, 20% of which are roses. Let X be the number of roses that Sally picks, and let Y be the number of roses that the couple picks altogether. Find the number of roses that we expect Sally to pick if the total number of roses picked is Y = 12. 5 6. Design your own problem and solution. Create your own problem about conditional expectation. 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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problemset37 - b Find E X 1 | X 2 = 0 4 5 Sally and David...

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