# rec09 - Let the random variables X and Y have a joint PD...

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Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 9 October 7, 2010 1. Let X be an exponential random variable with parameter λ > 0. Calculate the probability that X belongs to one of the intervals [ n,n + 1] with n odd. 2. (Example 3.13 of the text book, page 165) Exponential Random Variable is Memoryless. The time T until a new light bulb burns out is an exponential random variable with parameter λ . Ariadne turns the light on, leaves the room, and when she returns, t time units later, Fnds that the bulb is still on, which corresponds to the event A = { T > t } . Let X be the additional time until the bulb burns out. What is the conditional CD± of X , given the event A ? 3. Problem 3.23, page 191 in the text.
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Unformatted text preview: Let the random variables X and Y have a joint PD which is uniform over the triangle with vertices (0 , 0), (0 , 1), and (1 , 0). (a) ind the joint PD of X and Y . (b) ind the marginal PD of Y . (c) ind the conditional PD of X given Y . (d) ind E [ X | Y = y ], and use the total expectation theorem to Fnd E [ X ] in terms of E [ Y ]. (e) Use the symmetry of the problem to Fnd the value of E [ X ]. 4. We have a stick of unit length, and we break it into three pieces. We choose randomly and independently two points on the stick using a uniform PD, and we break the stick at these points. What is the probability that the three pieces we are left with can form a triangle? Page 1 of 1...
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## This note was uploaded on 12/02/2011 for the course ENGINEERIN EE302 taught by Professor Proasin during the Spring '11 term at South Carolina.

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