Question

TOPIC: Random variables with bounded range

Suppose a random variable X can take any value in the interval [−1,2] and a random variable Y can take any value in the interval [−2,3].

QUESTION 1: The random variable X−Y can take any value in an interval [a,b]. Find the values of a and b:

a=

b=

QUESTION 2 (Yes or No): Can the expected value of X+Y be equal to 6?

Answer 1

Question 1

The random variable X-Y would take any value in the interval [a,b]

To find 'a' we can take leftmost value of X and rightmost value of Y

a = -1 - 3 = -4

To find 'b' we take rightmost value of X and leftmost value of Y

b = 2 - (-2) = 4

Question 2

No. The expected value of X + Y could never be 6. The maximum value of X is 2 and of Y is 3. So maximum value of X + Y = 5. This expected value can not be beyond the range of value the random variable takes.