What are the mean and standard deviation of a probability

segnverd3a

segnverd3a

Answered question

2022-01-30

What are the mean and standard deviation of a probability density function given by Pr(X=k)=9ke9k! for k{0,1,2...}?

Answer & Explanation

seibesitoeu

seibesitoeu

Beginner2022-01-31Added 12 answers

Explanation: this pdf is a Poisson distribution XPo(λ) P(X=k)=λkekk!,k{0,1,2,3,4,...} In such cases the mean (E(X)) and variance (Var(X)) are given by E(X)=λ,Var(X)=λ In this case we have P(X=k)=9ke9k!,k{0,1,2,3,4,...} so E(X)=9 Var(X)=9 sd=Var=9=3

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