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.