Question

Et X be a discrete random variable whose probability mass function is P(X=x) = 4/3(3/7)^x, x=1,2,3...

Is this probability mass function a valid probability mass function? If so, verify that the probability mass function P(X=x) is a valid probability mass function.

Answer 1

The given probability mass function is valid if it satisfies two conditions: P(x) is between 0 and 1, inclusive, and the sum of probabilities is equal to 1.

Step-by-step explanation:

The given probability mass function is

P(X=x) = 4/3(3/7)^x for x=1,2,3...

To determine if this is a valid probability mass function, we need to check two conditions:

1. P(x) is between 0 and 1, inclusive: Here, the given function satisfies this condition because 4/3(3/7)^x will always be between 0 and 1 for any value of x. Hence, the probability is valid.
2. The sum of probabilities is equal to 1: To verify this, we can find the sum of probabilities for all possible values of x. Since the given function is exponential, we can use the formula for the sum of an infinite geometric series to find the sum.