Question

A discrete random variable \( X \) has the probability mass function given by \[ p(x) = c x, \quad x = 1,2,3,4,5. \] The value of the constant \( c \) is:

• A. \( \frac{1}{5} \)
• B. \( \frac{1}{10} \)
• C. \( \frac{1}{15} \)
• D. \( \frac{1}{20} \)

Hint:

The sum of all probability mass function (PMF) values must be 1. Use: \[ \sum p(x) = 1 \] to determine the constant.

Answer 1

The Correct Option is C

Step 1: Using the probability condition. The total probability must sum to 1: \[ \sum p(x) = 1. \]
Step 2: Computing \( c \). \[ \sum_{x=1}^{5} c x = 1. \] \[ c (1 + 2 + 3 + 4 + 5) = 1. \]
Step 3: Solving for \( c \). \[ c (15) = 1 \quad \Rightarrow \quad c = \frac{1}{15}. \]
Step 4: Selecting the correct option. Since \( c = \frac{1}{15} \), the correct answer is (C).