Question

If the probability function for a random variable \( x \) is given as \( f(x) = \frac{x+3}{15} \) when \( x = 1, 2, 3 \), find the sum of the values of the probability distribution for \( x \).

• A. 0.75
• B. 0.85
• C. 0.95
• D. 1.0

Hint:

The sum of the probabilities of a discrete random variable must always be 1.

Answer 1

The Correct Option is D

Step 1: Understand the sum of probabilities.
The sum of the probabilities for a discrete random variable must always be equal to 1. The probability mass function is given as: \[ f(x) = \frac{x+3}{15} \text{for } x = 1, 2, 3. \] We need to check if the sum of probabilities equals 1.

Step 2: Calculate the probabilities.
- For \( x = 1 \), \( f(1) = \frac{1+3}{15} = \frac{4}{15} \) - For \( x = 2 \), \( f(2) = \frac{2+3}{15} = \frac{5}{15} \) - For \( x = 3 \), \( f(3) = \frac{3+3}{15} = \frac{6}{15} \)

Step 3: Check the sum.
The sum of the probabilities is: \[ \frac{4}{15} + \frac{5}{15} + \frac{6}{15} = \frac{15}{15} = 1. \]

Step 4: Conclusion.
The sum of the probabilities is 1, so the correct answer is (D).