Question

Let X be the outcome of a roll of a 6-sided die, with possible values 1,2,3,4,5,6, and let Y be the outcome of a roll of a 10-sided die, with possible values 1,2,3,4,5,6,7,8,9, and 10.

Explain briefly why X and Y are not identically distributed.

Answer 1

We know that two random variables X and Y can only be identically distributed when X{E[x],V[x]} is equal to Y{E[y], V[y]}

we know that when the data elements increases in a sample, then the mean and variance are changed

So, E[x] and V[x] for random variable X must be different from E[y] and V[y] for random variable Y because random variable X has only 6 outcomes whereas random variable Y has 10 outcomes

therefore, we can say that X and Y are not identically distributed because they have different probability distribution