Question

The c.d.f. $F(x)$ of a discrete random variable $X$ is given by
\[ \begin{array}{c|cccccccc} X & -3 & -1 & 0 & 1 & 3 & 5 & 7 & 9 \\ F(X) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \end{array} \] Then $P(X=3)=$

• A. $0.85$
• B. $0.10$
• C. $0.75$
• D. $0.65$

Hint:

For discrete variables, probability at a point equals the jump in the CDF at that point.

Answer 1

The Correct Option is B

Step 1: Using the definition of probability from CDF.
For a discrete random variable, \[ P(X=a)=F(a)-F(a^-) \]
Step 2: Applying the formula.
\[ F(3)=0.75,\quad F(1)=0.65 \] \[ P(X=3)=0.75-0.65=0.10 \]
Step 3: Conclusion.
The required probability is $0.10$.