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?