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MAT521-2006Spring

# MAT521-2006Spring - May 4,2006'nd-OO M AT 5 21 F inal E xam...

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May 4,2006 ¥"'nd.-OO" MAT 521, Final Exam ~CCl~ NAME: Instructions: There are 9 problems in this exam for a grand total of 90 points. Each problem is worth about 10 points. Be sure to show your work and explain your reasoning. In general, incomplete or incorrect answers may receive no credit. 1. (12 points) Let X be a random variable with probability density function l<x<oo fix) = { :' otherwise. (a) Find Pr(X :s; 2). (b) Find E(X) and Var(X).

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2 . 1 (c) Let Y = X. Find the probability density function of Y. Be sure your answer is complete! 2. (10 points) A random variable X has distribution function F(x) = 1 - e- z / 5 for -00 < x < 00. (Do not simplify your answer.) Find Pr(5 < X < 10) and also the p.d.f. of X.
3 3.- (8 points) A random variable X has mean 5 and variance 16. Find numbers a and b such that Y has X-a mean 0 and variance 1, where Y = b 4. (10 points) There are 20 rotted apples in a crate containing 100. Someone picks at random a sample of 20 and without replacement. What is the probability that exactly 5 are rotted? I want the answer as a decimal. Explain which distribution you are using.

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MAT521-2006Spring - May 4,2006'nd-OO M AT 5 21 F inal E xam...

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