Re: What is expected value and variance here?

"Cool Giraffe" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED]
> I got help in another thread and the only problem
> that remains is this.
>
> f(x) = f(x) = (  e^(-x)  *  x^(a)  )  /  (  a!  )
> is a density function of X.
> How to compute the variance of X? I'm guessing that
> the expected value and variance are the same in this
> case since it is similar to X~Po(lambda) but i don't see
> how to show it. Any hints?
>
> Also - thanks to Dirk VdM, by the way.

You are welcome :-)
The expected value and variance for the gamma distribution
are easily calculated using the definition of the gamma function.

E[X] = int( x*f(x) )         int from 0 to infinity
  = 1/a! * int( x^(a+1) * exp(-x) )
  = 1/a! * gamma(a+2)
  = 1/a! * (a+1)!      because a is integer
  = a+1

E[X^2] = int( x^2*f(x) )         int from 0 to infinity
  = 1/a! * int( x^(a+2) * exp(-x) )
  = 1/a! * gamma(a+3)
  = 1/a! * (a+2)!      because a is integer
  = (a+2)*(a+1)

VAR[X] = E[X^2] - E[X]^2
  = (a+2)*(a+1) - (a+1)^2
  = (a+1)

hth, again :-)

Dirk Vdm



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> Vänligen
> Kerstin Käll (The Giraffe)
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