If the p.d.f. of a random variable X is f(x)= cc 0.5 x, & 0 x 2 0… - Vidyadip

MCQ

If the p.d.f. of a random variable X is
$\mathrm{f}(x)=\left\{\begin{array}{cc}0.5 x, & 0 \leq x \leq 2 \\ 0, & \text { otherwise }\end{array}\right.$
then the value of $\mathrm{P}(0.5 \leq \mathrm{X} \leq 1.5)$ is

A
$\frac{1}{4}$
✓
$\frac{1}{2}$
C
$\frac{3}{4}$
D
1

✓

Answer

Correct option: B.

$\frac{1}{2}$

(B)
$\mathrm{P}(0.5 \leq \mathrm{X} \leq 1.5)=\int_{0.5}^{1.5} \mathrm{f}(x) \mathrm{d} x=\int_{0.5}^{1.5} 0.5 x \mathrm{~d} x$
$=0.5\left[\frac{x^2}{2}\right]_{0.5}^{1.5}=\frac{1}{2}$

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