Let X1 and X2 be jointly distributed with pdf f(x1,x2)=begincasestfrac141+x1x2(x1^2-x2^2), & x1<1, x2<1, 0, & otherwise.endcases Then, the characteristic function of X1 is:

Q11Section I (General (compulsory))11 of 84

The odd term integrates out, leaving $X_1\sim U(-1,1)$

Let $X_1$ and $X_2$ be jointly distributed with pdf

$f(x_1,x_2)=\begin{cases}\tfrac14\bigl\{1+x_1x_2(x_1^2-x_2^2)\bigr\}, & |x_1|<1, |x_2|<1,\ 0, & \text{otherwise.}\end{cases}$

Then, the characteristic function of $X_1$ is:

Pick an option to check your answer.

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