Question

The cumulative distribution function of a discrete random variable X is given. Then $\frac{P(X \le 0)}{P(X > 0)} = $ ______.

• A. $\frac{1}{2}$
• B. 1
• C. $\frac{1}{3}$
• D. $\frac{1}{5}$

Hint:

Never recalculate individual Probability Mass Function (PMF) values if you are given the Cumulative table! $P(X \le k)$ is just a straight lookup: it is simply the number printed exactly under $k$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
By definition, the Cumulative Distribution Function (CDF), $F(x)$, represents $P(X \le x)$. The probability of the complement event $P(X > x)$ is $1 - F(x)$.

Step 2: Formula Application:
$P(X \le 0) = F(0)$ $P(X > 0) = 1 - P(X \le 0) = 1 - F(0)$

Step 3: Explanation:
From the table, $F(0) = 0.5$. Therefore, $P(X \le 0) = 0.5$. $P(X > 0) = 1 - 0.5 = 0.5$. The ratio is $\frac{0.5}{0.5} = 1$.

Step 4: Final Answer:
The value of the ratio is 1.