Question

Probability density function of a random variable x is given below:

$f\left(x\right)=(\begin{array}{cc}0.25\mathrm{if}& 1\le x\le 5\\ 0& \mathrm{otherwise}\end{array}$

$P(x\le 4)$ is

• A. $\frac{3}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

The correct option is A $\frac{3}{4}$

Given probability density function is

$f\left(x\right)=(\begin{array}{cc}0.25\mathrm{if}& 1\le x\le 5\\ 0& \mathrm{otherwise}\end{array}$

$P(x\le 4)={\int }_{-\infty }^{4}f\left(x\right)dx$

$={\int }_{-\infty }^{1}f\left(x\right)dx+{\int }_1^{4}f\left(x\right)dx$

$={\int }_{-\infty }^1\left(0\right)dx+{\int }_1^4\left(0.25\right)dx$

$=0+\frac{1}{4}[x{]}_1^4$

$=\frac{3}{4}$