# The expected value of a random variable raised to a power of more than two

I have come across a question that asks me to find $$E((1+X)^3)$$. The only values given in the question are $$E(X)$$ and $$E(X^2)$$ and I tried to solve it by expanding $$(1+X)^3$$. But with this approach, I have an $$E(X^3)$$ term that I don't know how the find the value of. Any help would be much appreciated.

Edit: The values of $$E(X)$$ and $$E(X^2)$$ are 1 and 4 respectively.

• What are $E(X)$ and $E(X^2)$? Commented Apr 19, 2019 at 8:38
• Do you know anything else about $X$? Commented Apr 19, 2019 at 8:41
• You cannot find $EX^{3}$ and $E(1+X)^{3}$ from the given data. May be you are not quoting the question you came across properly. Commented Apr 19, 2019 at 8:42
• Is anything known about the distribution of $X$? If there is no further info then the question cannot be answered. Random variables $X_1,X_2$ can be constructed with $\mathbb EX_1=1=\mathbb EX_2$ and $\mathbb EX_1^2=4=\mathbb EX_2^2$ and $\mathbb E(1+X_1)^3\neq\mathbb E(1+X_2)^3$. Commented Apr 19, 2019 at 9:09
• See also this question: math.stackexchange.com/questions/3191938/… In that question $E(X)^2 = E(X^2)$ such that $X$ was constant and $E(X^3) = E(X)^3$. Maybe you misread the question Commented Apr 19, 2019 at 9:27