Question

The probability mass function of a random variable \(X\) is given by \[ P(X = x) = \frac{5cx}{2^5}, \quad x = 0,1,2,3,4,5 \] \[ P(X = x) = 0, \quad \text{otherwise} \] Then find \(P(X \le 2)\).

• A. \(P(X>3)\)
• B. \(P(X \ge 3)\)
• C. \(P(X \ge 2)\)
• D. \(P(X>4)\)

Hint:

When probabilities involve ranges, always check if the complement gives a simpler expression.

Answer 1

The Correct Option is B

Step 1: Use the property of probability.
Since the total probability is 1, \[ P(X \le 2) = 1 - P(X \ge 3) \]
Step 2: Express the probability correctly.
The events \(X \le 2\) and \(X \ge 3\) are complementary for the given range of \(X\).

Step 3: Final conclusion.
Thus, \[ P(X \le 2) = P(X \ge 3) \]