Question

Let the pmf of x be defined by x/9 for x = 2, 3, 4. What is the probability mass function (pmf) of x?

1) x/9 for x = 2, 3, 4
2) x/9 for x = 2, 3
3) x/9 for x = 3, 4
4) x/9 for x = 2, 4

Answer 1

The probability mass function (pmf) of x is x/9 for x = 2, 3, 4. To calculate probabilities, we need to sum up the probabilities for each value of x. The correct answers for the given questions are 1/3, 5/9, and 1 respectively.

Step-by-step explanation:

The probability mass function (pmf) of x is given by x/9 for x = 2, 3, 4. So the correct option is 1) x/9 for x = 2, 3, 4.

To calculate probability, we need to sum up the probabilities for each value of x. Using the given pmf, we can calculate the probabilities as follows:

1. P(x = 3) = (3/9) = 1/3
2. P(0 < x < 3) = P(x = 2) + P(x = 3) = (2/9) + (3/9) = 5/9
3. P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4) = (2/9) + (3/9) + (4/9) = 9/9 = 1

Therefore, the correct answers are:

1. RF(x = 3) = 1/3
2. RF(0 < x < 3) = 5/9
3. RF(x ≥ 2) = 1