Q81 / 150 · MHT CET 2025 (26 Apr Shift 1) · Mathematics

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

  • A
    $\frac{1}{2}$
  • Correct answer
    B
    1
  • C
    $\frac{1}{2}$
  • D
    $\frac{1}{2}$

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 $\boxed{\text{B}}$.

Hence, the correct answer is option: 'B'.

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