The cumulative distribution function of a discrete random variable $X$ is $\begin{aligned}…

The cumulative distribution function of a discrete random variable $X$ is $\begin{aligned} \begin{array}{|r|c|c|c|c|c|c|c|c|} \hline X=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline F(X=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} \end{aligned}$ then $\frac{P(X \leq 0)}{P(X>0)}=$
  1. $\frac{1}{2}$
  2. 1
  3. $\frac{1}{2}$
  4. $\frac{1}{2}$

Solution

Given the cumulative distribution function $F(x) = P(X \leqslant x)$, we have $P(X \leqslant 0) = F(0) = 0.5$.

To find $P(X > 0)$, observe that $P(X > 0) = 1 - P(X \leqslant 0) = 1 - 0.5 = 0.5$.

The required ratio is therefore $\frac{P(X \leqslant 0)}{P(X>0)} = \frac{0.5}{0.5} = 1$.

The correct option is $\boxed{\text{B}}$.

Asked in: MHT CET 2025 (26 April Shift 1)

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