Question

For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true): Let X and Y be two binomial random variables. (a) If X and Y are independent, then X+Y is also a binomial random variable.

Answer 1

Answer:

yes

Step-by-step explanation:

it is absolutely true that biononmials always gives biononmials when added

Answer 2

If X and Y are independent, then X+Y is not a binomial random variable and so it is a false statement.

What is the sum of independent binomial random variables?

This term is known to be a binomial random variable that occurs when all the parts of the variables is said to have similar success probability.

The best method to check if two random variables are said to be independent is through the  calculation of the covariance of the two specific random variables.

Note that if If the variables are said to be independent (X and Y), then their difference is said to be not binomially distributed.

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