Problem 13 10 points Provide an example of a pair of random

Problem 1.3. (10 points) Provide an example of a pair of random variables which are identically distributed, but not equal.

Solution

Let X be the no of heads in six tosses and Y be the no of tails in those six tosses. Then X and Y have identical distribution, but they are not equal i.e., X=6-Y.

Here, X and Y are identically distributed but not equal.

Two variables are equal if and only if P(X=Y)=1, then we ca n say, X= Y.

If two random variables are equal then they have same distribution. But random variables identically (same) distributed need not be equal.