Prac_Quiz2 - Statistics 561 Study problems for 10/23...

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Unformatted text preview: Statistics 561: Study problems for 10/23 quiz (not to hand in) 1. A random variable X1 has pdf f1(ar;), mean it}, variance of, and moment—generating function M105). A random variable X2 has pdf f2(.1:), mean #2, variance 0%, and moment— generating function M26). Let Z be a random variable with pdf pffim) + (1 — p)f2(x), where O < p < 1. 8.. Find the mean of Z. b. Find the moment~generating function of Z. c. Find the variance of Z in terms of #1, pg, (7%, 0%, and p. 2. Find the moment—generating function corresponding to a. fist) = 1/0, 0 <3 < c. 1). fix) I 2.12/82, 0 < m < c. 3. Find P(X12 < X2 < X1) if X1 and X2 are jointly distributed with pdf f($1,$2):2$1. US$1S1, U<$2SL 4. -6. Text, p. 91-93: 2.2.14, 2.2.20, and 2.3.7. ...
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