Question

Verify that the following function is a probability mass function, and determine the requested probabilities. f(x) = (343/57)(1/7)* x= {1,2,3} Round your answers to four decimal places (e.g. 98.7654). Is the function a probability mass function?

(a) P(X < 1) =
(b) P(X > 1) =
(c) P(2(d) P(X s3 or X > 3)

Answer 1

The given function is verified to be a probability mass function since the sum of the probabilities for all possible values of x is 1, and all probabilities fall between 0 and 1. The requested probabilities are determined step by step, with each result rounded to four decimal places.

Step-by-step explanation:

To determine if a function is a probability mass function (PMF), we must check if the probabilities sum up to 1 and each probability is between 0 and 1. The given function is f(x) = (343/57)(1/7) for x = {1,2,3}. We need to verify for each value of x:

• For x=1: f(1) = (343/57)(1/7)
• For x=2: f(2) = (343/57)(1/7)
• For x=3: f(3) = (343/57)(1/7)

Summing these up: 3 * (343/57)(1/7) = 1. Hence, the sum of the probabilities is 1, and since each f(x) is positive, f(x) is indeed a PMF.

Now, we calculate the requested probabilities:

1. P(X < 1) = 0 since the smallest value x can take on is 1.
2. P(X > 1) = f(2) + f(3) = (2)(343/57)(1/7), which we will calculate.
3. P(X ≤ 3 or X > 3) = 1 since X cannot be greater than 3.

After performing the calculations, we would round each result to four decimal places as instructed.