The cumulative distribution function of a continuous random variable $\mathrm{X}$ is given by $F(X=x)=\frac{\sqrt{x}}{2}$, then $P[X1]$ is

Question

The cumulative distribution function of a continuous random variable $\mathrm{X}$ is given by $F(X=x)=\frac{\sqrt{x}}{2}$, then $P[X>1]$ is

Aicharya · Accepted Answer

Given c.d.f. is $f(x)=\frac{\sqrt{x}}{2}$ $\begin{aligned} 	herefore P(0) &=0 	ext { and } P(1)=\frac{1}{2} \ P[x>1] &=1-P[x \leq 1] \ &=1-\left(0+\frac{1}{2}ight)=\frac{1}{2} \end{aligned}$

The cumulative distribution function of a continuous random variable $\mathrm{X}$ is given by…

Solution