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}?

Dec 4, 2016

$E \left(X\right) = 10$

$s d = \sqrt{10}$

Explanation:

This is a Poisson distribution.

the standard eqn is:

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

For $k \in$$\left\{0 , 1 , 2 , 3 , 4. . \infty\right\}$

where mean$\text{ "E(X)=lambda;" }$ Variance$\text{ } V a r \left(X\right) = \lambda$

in this case

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

For $k \in$$\left\{0 , 1 , 2 , 3 , 4. . \infty\right\}$

$\therefore E \left(X\right) = 10$

$V a r \left(X\right) = 10$

$\therefore s d = \sqrt{10}$