What are the mean and standard deviation of a probability density function given by #Pr(X=k) = (80^ke^-80)/(k!) # for #k in {0,1,2... oo}#?

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Answer 1 · 2016-10-17T11:49:44

#E(X)=80, Var(X)=80#
#sd=sqrt80#

#P(x=k)=(80^ke^-80)/(k!) , k in {0,1,2,3.....oo}#

is a Poisson distribution, the standard formula being:

#P(x=k)=(lambda^ke^-lambda)/(k!), k in {0,1,2,3.....oo}#

the mean and variance are given by

# E(X)=lambda#
#Var(X)=lambda#
the proof of these results can be found from a search on the web.

the sd is the square root of the variance hence the results

#E(X)=80, Var(X)=80#
#sd=sqrt80#