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Unformatted text preview: Stat 400 In Class Worksheet 10 T.A. Emily King April 16, 2008 1. (Modified from book p. 202 # 27) Annie and Alvie have agreed to meet for lunch between noon (0:00 PM) and 1:00 PM. Denote Annie's arrival time by X, Alvie's by Y and suppose that X and Y are independent with pdf's fX (x) 3x2 = 0 2y = 0 0x1 o.w. 0y1 o.w. fY (y) Set up, but do not solve, the integral to compute the expected amount of time that the one who arrives first must wait for the other person. Also, what is ? 2. (Book Example 5.18) Let X and Y be discrete rv's with joint pmf 1 (x, y) = (-4, 1), (4, 1), (2, 2), (-2, -2) 4 p(x, y) = 0 o.w. What is the covariance of X and Y ? 3. (Modified from book p. 212 # 41) Let X be the number of packages being mailed to a randomly selected customer at a certain shipping facility. Supposed the distribution of X is as follows: x 1 2 3 p(x) .5 .3 .2 (a) Consider a random sample of size n = 2 and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. (b) Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between largest and smallest values in the sample). Obtain the distribution of R. 4. (Book p. 225, # 83) Let denote the true pH of a chemical compound. A sequence of n independent sample pH determinations will be made. Suppose each sample pH is a identically distributed random variable with expected value and standard deviation .1. How many determinations are required if we wish the probability that the sample average is within .02 of the true pH to be at least .95? What theorem justifies your probability calculation? ...
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