Question: The joint density function of the discrete trivariate random variable (left(X_{1}, X_{2}, X_{3}ight)) is given by [begin{aligned} fleft(x_{1}, x_{2}, x_{3}ight)= & .20 I_{{0,1}}left(x_{1}ight) I_{{0,1}}left(x_{2}ight) I_{left{left|x_{1}-x_{2}ight|ight}}left(x_{3}ight)

The joint density function of the discrete trivariate random variable $\left(X_{1}, X_{2}, X_{3}ight)$ is given by

\[\begin{aligned}

f\left(x_{1}, x_{2}, x_{3}ight)= & .20 I_{\{0,1\}}\left(x_{1}ight) I_{\{0,1\}}\left(x_{2}ight) I_{\left\{\left|x_{1}-x_{2}ight|ight\}}\left(x_{3}ight) \\

& +.05 I_{\{0,1\}}\left(x_{1}ight) I_{\{0,1\}}\left(x_{2}ight) I_{\left\{1-\left|x_{1}-x_{2}ight|ight\}}\left(x_{3}ight) .

\end{aligned}\]

a. Are $\left(X_{1}, X_{2}ight),\left(X_{1}, X_{3}ight)$, and $\left(X_{2}, X_{3}ight)$ each pairwise independent random variables?

b. Are $X_{1}, X_{2}, X_{3}$ jointly independent random variables?

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