340f_fall09 - 1. Suppose that the three inspectors at a...

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Unformatted text preview: 1. Suppose that the three inspectors at a film factory are supposed to stamp the expiration data on each package of film at the end of assembly line. John , who stamps 25% of the packages, fails to stamp the expiration date once in every 200 packages, Tom , who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages, Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages. If a customer complains that her package does not show the expiration date, what is the probability that was inspected by John? 2.Ten people are randomly seated at round table. What is the probability that a particular couple will seat next to each other? 3. The life span in hours of an electrical component is a random variable with cumulative distribution function 1 − e−x/50 x > 0 F (x) = 0 x<0 a. Find and sketch the pdf of X . b. Find the standard deviation of X . 4. Suppose the random variables X and Y are jointly distributed according to the pdf 3 fX,Y (x, y ) = (x2 + y 2 ), 0 < x < 1, 0 < y < 1 2 Find a) fX (x) b) P (X < Y ) c) P (Y < 1/2|X = 1/2) 5. Suppose that the random variable X has moment generating function 0.25et MX (t) = 1 − (1 − 0.25t)et . a. Find variance using moment generating function. b. Find P (2 < X ≤ 4). 6. The driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 36450 pounds. If the distribution of the weight of a box has a mean of 40 pounds and a variance of 36, find the approximate probability that the driver will not be fined. 1 ...
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This note was uploaded on 09/19/2011 for the course MATH 340 taught by Professor Staff during the Spring '08 term at S.F. State.

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