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Unformatted text preview: 1 } and let Z = ( Z 1 ,Z 2 ) be independent of X and have the same distribution. Give the joint density of X + Z . 4. A fair coin is tossed 100 times and then tossed again as many times as tails were obtained in the rst 100 tosses. Let X be the total heads tossed. Find the mean and variance of X in as simplied a form as possible (decimal form is best). 5. (a) Find the density of the median of three independent uniform (0 , 1) variables. (b) Is there a density g such that if X 1 ,X 2 ,X 3 are independent and have density g then the median of the X i has a uniform (0 , 1) distribution?...
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This document was uploaded on 01/25/2012.
- Spring '09