# Discrete probability distributions

1. Aug 1, 2014

### somecelxis

1. The problem statement, all variables and given/known data
Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?

2. Relevant equations

3. The attempt at a solution

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2. Aug 1, 2014

### Ray Vickson

$\text{Var}(X-2) = \text{Var}(X)$ because $\text{Var}(\cdot)$ is unaffected by a non-random shift. Also: $\text{Var}(X) = E(X^2) - (EX)^2$.

3. Aug 2, 2014

4. Aug 2, 2014