What are the mean and standard deviation of a probability density function given by #Pr(X=k) = (10^ke^-10)/(k!) # for #k in {0,1,2... oo}#?

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Answer 1 · 2016-12-04T15:15:01

#E(X)=10#

#sd=sqrt10#

This is a Poisson distribution.

the standard eqn is:

#X~P(lambda)=>P(X=k)=(lambda^ke^-lambda)/(k!)#

For #k in ##{0,1,2,3,4..oo}#

where mean#" "E(X)=lambda;" "# Variance#" "Var(X)=lambda#

in this case

#P(X=k)=(10^ke^-10)/(k!)#

For #k in ##{0,1,2,3,4..oo}#

#:.E(X)=10#

#Var(X)=10#

#:.sd=sqrt10#