Solutions - 5100-03

(1) Find the PMF of $X$ from the CDF:

$k$	0	1	2	3
$P_X(k)$	0.1	0.1	0.3	0.5

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(2) Find the PMF of $Y=3X$:

Since $Y=3X$, the possible values of $Y$ are $3\cdot 0=0$, $3\cdot 1=3$, $3\cdot 2=6$, $3\cdot 3=9$, each with the same probability as the corresponding $X$ value.

$k$	0	3	6	9
$P_Y(k)$	0.1	0.1	0.3	0.5