Random variable X with mean $E(X)=7$ and $var(X)=6$. Calculate $E((X-a)^2)$?

Question

I have looked for answer long time and given hints are that mean is $E(Y)=E(ag(X)+bh(X))$ and variance for random variable X is $var(X)=E(X^2)−[E(X)]^2$. I hope someone could help me with my problem.

Thanks for your answers!

Answer 1

Hint:

1. $Var(X-a)=Var(X)$
2. $E(X-a)=E(X)-a$
3. $Var(X-a)=E((X-a)^2)-(E(X-a))^2$

Can you use these in the correct order?

Answer 2

$(X-a)^2 = X^2 - 2Xa + a^2\\ E[(X-a)^2] = E[X^2] - 2a E[X] + a^2\\ Var X = E[X^2] - E[X]^2$

And that should be enough to substitute what you know to find what you don't know.