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#