# rec11 - q ) , if 0 q 1 , , otherwise . This Q represents...

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Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 11 October 14, 2010 1. Let X be a discrete random variable that takes the values 1 with probability p and - 1 with probability 1 - p . Let Y be a continuous random variable independent of X with the Laplacian (two-sided exponential) distribution f Y ( y ) = 1 2 λe - λ | y | , and let Z = X + Y . Find P ( X = 1 | Z = z ). Check that the expression obtained makes sense for p 0 + , p 1 - , λ 0 + , and λ → ∞ . 2. Let Q be a continuous random variable with PDF f Q ( q ) = b 6 q (1 -
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Unformatted text preview: q ) , if 0 q 1 , , otherwise . This Q represents the probability of success of a Bernoulli random variable X , i.e., P ( X = 1 | Q = q ) = q. Find f Q | X ( q | x ) for x { , 1 } and all q . 3. Let X have the normal distribution with mean 0 and variance 1, i.e., f X ( x ) = 1 2 e-x 2 / 2 . Also, let Y = g ( X ) where g ( t ) = b-t, for t 0; t, for t > , as shown to the right. Find the probability density function of Y .-5 5 1 2 3 4 5 t g(t) 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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