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In case you get stuck computing the integrals referred to in the above post, here is an automated way to proceed. Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$. The mean $E_f[N]$ is:

and the variance of $N$ is:

where I am using the Expect and Var functions from the the mathStatica package for Mathematica to automate the nitty-gritties.

In the case of $\theta = 4$, the above results simplify to $E[N] = y$ and $Var(N) = y^2$.

In case you get stuck computing the integrals referred to in the above post, here is an automated way to proceed. Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$. The mean $E_f[N]$ is:

and the variance of $N$ is:

where I am using the Expect and Var functions from the the mathStatica package for Mathematica to automate the nitty-gritties.

In the case of $\theta = 4$, the above results simplify to $E[N] = y$ and $Var(N) = y^2$.

Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$. The mean $E_f[N]$ is:

and the variance of $N$ is:

where I am using the Expect and Var functions from the the mathStatica package for Mathematica to automate the nitty-gritties.

In case you get stuck computing the integrals referred to in the above post, here is an automated way to proceed. Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$. The mean $E_f[N]$ is:

and the variance of $N$ is:

where I am using the Expect and Var functions from the the mathStatica package for Mathematica to automate the nitty-gritties.

In the case of $\theta = 4$, the above results simplify to $E[N] = y$ and $Var(N) = y^2$.

Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$.

Then, using the mathStatica package for Mathematica, the mean $E[N]$ is:

and the variance of $N$ is:

Given random variable $N$ has pdf $f(n)$:

The density is well-defined provided $\theta>1$. The mean $E_f[N]$ is:

and the variance of $N$ is:

where I am using the Expect and Var functions from the the mathStatica package for Mathematica to automate the nitty-gritties.