Discrete probability distributions

[somecelxis]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

 

[ehild]

Homework Statement

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?

You made a mistake when expanding (x-2)².

ehild

 

[Ray Vickson]

Homework Statement

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?

You made a mistake when expanding (x-2)².

ehild

I guess I would have caught that if the OP had typed out his work, but since I never read attached thumbnails I missed it.