11ProbHw10

# 11ProbHw10 - X and diﬀerentiate to obtain a formula for...

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IEOR 3658 Assignment #10 Probability November 17, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #10 – due November 23rd, 2011 1. (From text) If X is a random variable that is uniformly distributed between -1 and 1, ﬁnd the PDF of p | X | and the PDF of - log | X | 2. (From text) Find the PDF of e X in terms of the PDF of X . Specialize the answer to the case where X is uniformly distributed between 0 and 1. 3. (From text) The metro train arrives at the station near your home every quarter hour starting at 6:00 am. You walk into the station every morning between 7:10 and 7:30 am, with the time in this interval being a random variable with given PDF. Let X be the elapsed time, in minutes, between 7:10 and the time of you arrival. Let Y be the time that you have to wait until you board a train. Calculate the CDF of Y in terms of the CDF of
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Unformatted text preview: X and diﬀerentiate to obtain a formula for the PDF of Y . 4. (From text) Let X and Y be the Cartesian coordinates of a randomly chosen point (according to a uniform PDF) in the triangle with vertices at (0,1), (0,-1), and (1,0). Find the CDF and the PDF of Z = | X-Y | . 5. A particle’s velocity V is modeled as a normal random variable with mean 0 and variance σ 2 (we allow negative values). The particle’s energy is given by W = m V 2 2 , where m > 0 is a constant. (a) What is E [ W ] in terms of m and σ ? (b) What is the PDF of W ? 6. Extra Credit: Two points are chosen randomly and independently from the interval [0 , 1] according to a uniform distribution. Show that the expected distance between the two points is 1/3....
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## This note was uploaded on 12/11/2011 for the course IEOR 3658 taught by Professor Olvera during the Fall '08 term at Columbia.

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