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Unformatted text preview: Math 310 [Porod)
Midterm II November 23, 2010 Time: 60 minutes
Instructions: No books, notes, calculators are permitted. Do all work and record all answers in the blue
book. Write your name and your instructor’s name on the front cover. 1. (21 points) Deﬁne the following terms. (a) The density function of the binomial distribution with n trials and success probability p;
(b) the density function of the Poisson distribution with parameter A; (c) the density function of the gamma distribution with parameters (or, A); (d) the density function of the normal distribution with parameters (n, 02); (e) the density function of the uniform distribution on the interval [a, h]; (f) the variance of a random variable; (9;) the covariance of two random variables. 2. (24 points) Let X , Y be independent random variables. Both have geometric distribution with
parameter p. Compute the following quantities: (a) E (X ) (you must show your work);
(b) E(3X) for the parameter p = g;
(c) the density of min(X, Y). 3. (24 points) For a certain repair company, the time T (in hours) required to repair a vacuum cleaner is an exponential random variable with parameter A : (a) What is the expected time for a repair? (b) What is the median time for a repair? (c) You drop off your vacuum Cleaner at the repair shop. After 2 hours you call in and are being
told that the repair hasn’t been completed yet. Compute the probability that the repair will
take more than 5 hours altogether. 4. (18 points) Let X be a random variable with density function % ifasE(0,5) fX($) = g—% ifa" 6 [5,10) 0 otherwise (a) Compute the distribution function FX.
(b) Let Y : X2. Find the density fy. 5. ( 13 points) Let X be a random variable with uniform distribution on the interval (— g, Deﬁne
Y = tan X. Compute the density fy. What is the name of the distribution of Y? ...
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 Spring '11
 SARVER

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