A random variable $X$ has the following probability distribution :

Find the (c)(d)f. of $X$

• A

  
  
  
• B

  
  
  
• Correct answer
  C

  
  
  
• D

  
  
  

Solution

$F(x)=P(X < x)$ $\begin{aligned} &F(0)=P(X \leq 0)=0.5 \\ &F(1)=P(X \leq 1)=0.5+0.2=0.7 \\ &F(2)=P(X \leq 2)=0.5+0.2+0.18=0.88 \\ &F(3)=P(X \leq 3)=0.5+0.2+0.18+0.12=1 \end{aligned}$ $\therefore$ The c.d.f. of $X$ is

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