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.

  • $\begingroup$ What are $E(X)$ and $E(X^2)$? $\endgroup$ Commented Apr 19, 2019 at 8:38
  • $\begingroup$ Do you know anything else about $X$? $\endgroup$ Commented Apr 19, 2019 at 8:41
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    $\begingroup$ 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. $\endgroup$ Commented Apr 19, 2019 at 8:42
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    $\begingroup$ 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 $\mathbb E(1+X_1)^3\neq\mathbb E(1+X_2)^3$. $\endgroup$
    – drhab
    Commented Apr 19, 2019 at 9:09
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    $\begingroup$ 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 $\endgroup$
    – Cettt
    Commented Apr 19, 2019 at 9:27


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