What are the mean and standard deviation of a probability density function given by $Pr(X=k) = (9^ke^-9)/(k!)$ for $k in {0,1,2... oo}$ ?

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Answer 1 · 2016-11-28T17:51:48

mean =9

sd=3

this pdf is a Poisson distribution

$X~Po(lambda)$

$P(X=k)=(lambda^ke^-k)/(k!)," " kin{1,2,3,4,...oo}$

In such cases the mean (E(X)) and variance (Var(X)) are given by

$E(X)=lambda," "Var(X)=lambda$

in this case we have

$P(X=k)=(9^ke^-9)/(k!)," " kin{1,2,3,4,...oo}$

so $" "E(X)=9$

$Var(X)=9$

$sd=sqrtVar=sqrt9=3$

What are the mean and standard deviation of a probability density function given by Pr(X=k) = (9^ke^-9)/(k!) Pr(X=k) = (9^ke^-9)/(k!) for k in {0,1,2... oo}k in {0,1,2... oo}?