(a) Let $X$ be the sum of the two numbers. Find the pdf of $X$ \begin{tabular}{1|ccccccccccc) $X=k$ & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 V \hline$f (k)$ & $\frac{1}{36}$ & $\frac{2}{36}$ & $\frac{3} {36}$ & $\frac{4}{36}$ & $\frac{5}{36}$ & $\frac{6}{36}$ & $\frac{5}{36}$ & $\frac{1}{36}$ & $\frac{3}{36}$ & $\frac{2} {36}$ & $\frac{1}{36}$ \end{tabular) Find $PX7)$ (b) Let $y$ be the larger number (in case of double, the number is considered the larger number. For example, $(3,3)$, then 3 is the larger number). Find the pdf, mean, variance. (c) Let $W$ be the absolute value of the difference of the two numbers. Find the pdf. SP.PB.083