RecitationFour - X N ( , 2 ) , with parameters and > , f...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications Recitation 4 Wednesday February 17, 2010 Some common random variables For each of the following random variables, plot the pdf or PMF and show that it integrates to one over all x ( or sums to one over all n ). Do not use any symbolic math program or numerical method. Work out the answer analytically. 1. Uniform random variable X U ( a, b ) ,with b>a , f X ( x ) , 1 b a [ u ( x a ) u ( x b )] . 2. Exponential random variable X , with parameter μ> 0 , f X ( x ) , 1 μ exp( x μ ) u ( x ) = 1 μ e x μ u ( x ) (alternative notation).
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Unformatted text preview: X N ( , 2 ) , with parameters and > , f X ( x ) , 1 2 exp[ 1 2 x 2 ] = 1 2 exp 1 2 x 2 (alternative notation). You can make use here of the known integral Z e x 2 2 dx = r 2 . 4. Binomial random variable K , with parameters n and p, n a positive integer and p 1 . De f ne q , 1 p. P K ( k ) , n k p k q n k , k n, , else. 5. Poisson random variable N, with paramter > , P N ( n ) , n n ! e u ( n ) . 1...
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This note was uploaded on 04/15/2010 for the course ECSE 4500 taught by Professor Woods during the Spring '08 term at Rensselaer Polytechnic Institute.

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