Unformatted text preview: X has a Poisson distribution with parameter λ if P ( X = i ) = eλ λ i i ! . Note ∑ ∞ i =0 λ i /i ! = e λ , so the probabilities add up to one. To compute expectations, E X = ∞ X i =0 ieλ λ i i ! = eλ λ ∞ X i =1 λ i1 ( i1)! = λ. Similarly one can show that E ( X 2 )E X = E X ( X1) = ∞ X i =0 i ( i1) eλ λ i i ! = λ 2 eλ ∞ X i =2 λ i2 ( i2)! = λ 2 , 16...
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 Spring '10
 ansan
 Variance, Probability theory, yi yj, E Yi Yj

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