rec15 - Massachusetts Institute of Technology Department of...

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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 15 October 28, 2010 1. Problem 6.14 (a)-(c),(h)-(j), page 330 in text. Beginning at time t = 0, we begin using bulbs, one at a time, to illuminate a room. Bulbs are replaced immediately upon failure. Each new bulb is selected independently by an equally likely choice between a type-A bulb and a type-B bulb. The lifetime, X , of any particular bulb of a particular type is a random variable, independent of everything else, with the following PDF: for type-A Bulbs: f X ( x ) = braceleftbigg e- x , x , , otherwise; for type-B Bulbs: f X ( x ) = braceleftbigg 3 e- 3 x , x , , otherwise. (a) Find the expected time until the first failure. (b) Find the probability that there are no bulb failures before time t . (c) Given that there are no failures until time t , determine the conditional probability that the first bulb used is a type-A bulb.first bulb used is a type-A bulb....
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