Question:
The cumulative distribution function of a discrete random variable X is
\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} \]
then \(\frac{P(X \leqslant 0)}{P(X>0)}=\)
The cumulative distribution function of a discrete random variable X is
\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} \]
then \(\frac{P(X \leqslant 0)}{P(X>0)}=\)
Show Hint
Read the cumulative probabilities at 0 and use the fact that the total probability is 1.
Updated On: Nov 13, 2026
\(\frac{1}{2}\)
1
\(\frac{1}{3}\)
\(\frac{1}{5}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The cumulative distribution function gives \(F(x)=P(X\leq x)\). So \(P(X\leq 0)=F(0)\) and \(P(X>0)=1-F(0)\).
Step 2: Read from the table
From the table, \(F(0)=0.5\).
Step 3: Calculation
\(P(X\leq 0)=0.5\) and \(P(X>0)=1-0.5=0.5\).
\(\dfrac{P(X\leq 0)}{P(X>0)}=\dfrac{0.5}{0.5}=1\)
Final Answer:
The required ratio is 1. \[ \boxed{\text{(B) }1} \]
The cumulative distribution function gives \(F(x)=P(X\leq x)\). So \(P(X\leq 0)=F(0)\) and \(P(X>0)=1-F(0)\).
Step 2: Read from the table
From the table, \(F(0)=0.5\).
Step 3: Calculation
\(P(X\leq 0)=0.5\) and \(P(X>0)=1-0.5=0.5\).
\(\dfrac{P(X\leq 0)}{P(X>0)}=\dfrac{0.5}{0.5}=1\)
Final Answer:
The required ratio is 1. \[ \boxed{\text{(B) }1} \]
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