Consider two random variables X and Y with the PMFs
pX(x) =
(
1/10 + a(x − 5)2, if x 2 {3, 4, 5, 6, 7}
0, o.w.
,
pY (y) =
(
3/10 − b(y − 3)2, if y 2 {1, 2, 3, 4, 5}
0, o.w.
.
(a) Find a and b.
(b) Evaluate 2X
and 2Y
. Which one is larger? Explain how you would reach the
same answer without calculating the variances.