# Thread: Consider two random variables X and Y with the PMFs

1. ## Consider two random variables X and Y with the PMFs

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.

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.
Please try and improve the statement of the question, that is almost incomprehensible.

To do part a) you need to use the result that for a random variable $U$:

$\sum p_U(u) =1$

(the sum of the probabilities of all the possible outcomes is 1)

CB