Question

Determine the mean and variance of the random variable with the following probability mass function. f(x) = (125/31)(1/5)^x ........ x = 1,2,3

LAST QUESTION I SWEAR!!!

Answer 1

`f(x)=\begin{cases}(125)/(31)&\text{for }x\in\{1,2,3\}\\\\0&\text{otherwise}\end{cases}`

The mean is


`\mathbb E(X)=\displaystyle(125)/(31)\sum_(x=1)^3x\left(\frac15\right)^x=(38)/(31)`

You then have


`\mathbb E(X^2)=\displaystyle(125)/(31)\sum_(x=1)^3x^2\left(\frac15\right)^x=(54)/(31)\approx1.74`

so the variance is


`\mathbb V(X)=(54)/(31)-\left((38)/(31)\right)^2=(230)/(961)\approx0.239`