# Basic Expected Value Problem (probability)

E[X]=2
Var(X)=3
Find E[4+4x+x^2]

I'm just confused what its asking. The expected value of this function is 2 so the average of it is 2 and the variance is how much it varies which is 3? Every example I have for expected values is related to an example such as cards, not just a polynomial

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Dick
Homework Helper
Var(X)=E(X^2-E(X)^2). Just solve that for E(X^2). Then you can find E of the quadratic.

Var(X)=E(X^2-E(X)^2). Just solve that for E(X^2). Then you can find E of the quadratic.
Is the E(X^2-E(X)^2) = E(2^2-(4+4x+X^2)^2)?

Dick
Homework Helper
No.... Var(X)=3=E(X^2)-E(X)^2. E(X)=2. What's E(X^2)?? E(4+4X+X^2)=E(4)+E(4X)+E(X^2). Right? Etc. Use the linearity properties of 'E'.

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No.... Var(X)=3=E(X^2)-E(X)^2. E(X)=2. What's E(X^2)?? E(4+4X+X^2)=E(4)+E(4X)+E(X^2). Right? Etc.
I think I'm mixing up the terms E(X^2) and e(X)^2. Which one is E[X]=2?

So E(X^2)=E(4)^2+E(4x)^2+(x^2)^2?

Dick
Homework Helper
E(X)^2=4, since E(X)=2.

E(X)^2=4, since E(X)=2.
Right but whats the difference between E(X^2) and E(X)^2?

Is E(X^2)=E(4^2)+E(4x^2)+E((x^2)^2) with x=2?

Dick
Homework Helper
No! E(X^2) is not the same as E(X)^2. They aren't directly related to each other. The only way you can find E(X^2) from the information you are given is to use Var(X)=3.

Var(X)+E(X)^2=E(X^2)
3+4=7=E(x^2)

Then use the fact that E(4+4X+X^2)=E(4)+E(4X)+E(X^2).

Dick