RecitationEight - a as (1 a ) a k u ( k ) with <...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications Recitation 8 Wednesday April 7, 2010 CommonMeansandVar iances discrete RVs Find the means and variances of the following discrete random variables. family pmf mean μ mean square variance σ 2 Bernoulli P B ( k )= ½ 1 ,p 0 ,q p p pq Binomial b ( k ; n, p )= ¡ n k ¢ p k q n k np ( np ) 2 + npq npq geometric 1 1+ μ ³ μ 1+ μ ´ k u ( k ) μ μ +2 μ 2 μ + μ 2 Poisson ( λT ) k k ! e λT u ( k ) λT ( λT ) 2 + λT λT q , 1 p
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Unformatted text preview: a as (1 a ) a k u ( k ) with < a < 1 . Then = a/ (1 a ) with > . Some useful de f nitions: mean-square value or average power : E [ X 2 ] variance : 2 = E [( X ) 2 ] = E [ X 2 2 X + 2 ] = E [ X 2 ] 2 E [ X ] + 2 = E [ X 2 ] 2 , since E [ X ] = . 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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