Question

Verify that the function is a probability mass function f(x) = (216/43) (1/6)ˣ, x={1,2,3}?

Answer 1

To verify if a function is a probability mass function, we need to check two conditions: the sum of probabilities must equal 1, and probabilities must be non-negative. By evaluating the function for each possible value of x, it can be determined that the given function satisfies both conditions and is a probability mass function.

Step-by-step explanation:

A probability mass function is a function that gives the probability of discrete random variables. To verify if the given function f(x) = (216/43) (1/6)ˣ, x={1,2,3} is a probability mass function, we need to check two conditions:

1. The sum of probabilities of all possible values of x must equal to 1.
2. The probability must be non-negative for all values of x.

Let's check these conditions:

1. When x=1, f(1) = (216/43) (1/6)¹ = (216/43) (1/6) = 36/43
2. When x=2, f(2) = (216/43) (1/6)² = (216/43) (1/36) = 6/43
3. When x=3, f(3) = (216/43) (1/6)³ = (216/43) (1/216) = 1/43

The sum of the probabilities is (36/43) + (6/43) + (1/43) = 43/43 = 1, which satisfies the first condition. The probabilities are all non-negative, which satisfies the second condition. Therefore, the given function f(x) is a probability mass function.