E(x) and Var(x): Let Y=-2X+3, X random, E(Y)=1, E(Y^2)=9; compute E(X) and Var(X)

[elioruzan]

Hi everyone.
I am stuck at a question that goes as follows:
X is a random variable. Let Y=-2X+3.
Given that E(Y)=1, E(Y^2)=9,
Compute E(X) and Var(X).
I found out E(X)=1 but couldn't find it's variety. Help will be appreciated!

 

[stapel]

X is a random variable. Let Y=-2X+3.
Given that E(Y)=1, E(Y^2)=9,
Compute E(X) and Var(X).
I found out E(X)=1

What were your steps?

but couldn't find it's variety.

Does "variety" perhaps mean "variation"?

Either way, please reply with a clear listing of your thoughts and efforts so far. Thank you!

Eliz.

 

[BigBeachBanana]

Hint: \(\displaystyle \text{Var}(aX + b) = a^2\text{Var}(X)\)

 

[elioruzan]

What were your steps?


Does "variety" perhaps mean "variation"?

Either way, please reply with a clear listing of your thoughts and efforts so far. Thank you!

Eliz.

Hi .
Thank you for your reply.
By variety i meant variance.
My steps so far:
1=E(y)=E(-2x+3)=-2E(x)+3
Therefore -2E(x)=-2
E(x)=1