Answer to Question #243488 in Statistics and Probability for hardik

Question

If X is a R.V with PDF f(x) = x/6 when x = 1, 2, 3 and f(x) = 0, otherwise. Find E(X+2)²

Answer 1

$$\begin{matrix} (x+2)^2 & 9 & 16 & 25 \\ p & 1/6 & 2/6 & 3/6 \end{matrix}$$

$$E[(X+2)^2]=9(\dfrac{1}{6})+16(\dfrac{2}{6})+25(\dfrac{3}{6})=\dfrac{58}{3}$$

$$E[(X+2)^2]=\dfrac{58}{3}$$