Question

Verify that the following function is a probability mass function f(x) = 343/57?

1) True
2) False

Answer 1

The function f(x) = 343/570 cannot be considered a valid probability mass function unless there is only one value that x can take, which is not provided in the context. Therefore, the statement is False.

Step-by-step explanation:

The given function f(x) = 343/570 is said to be a probability mass function (PMF). To verify whether it is a PMF, we need to ensure that two conditions are met:

• Each probability f(x) must be between 0 and 1, inclusive.
• The sum of all probabilities f(x) for all possible values of x must equal 1.

In this case, the function provided is a constant value, not a function that varies with x. If f(x) = 343/570 was meant to be the probability for each value of x in a discrete set, then the sum of all probabilities would exceed 1 if we have more than one value for x, which would violate the second condition for a PMF. Thus, without additional context suggesting that x can only take on one value (making it a degenerate distribution), we cannot consider this function to be a valid PMF. The assertion is therefore False.