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  4. If the probability density function of a random variable X is f(x) = (x/2) in 0 le x le 2, then P(X > 1.5 | X > 1) is equal to

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Q. If the probability density function of a random variable $X$ is $f(x)$ = $\frac{x}{2} in 0\le x \le 2,$ then $P\left(X > 1.5 | X > 1\right)$ is equal to

VITEEEVITEEE 2007Probability - Part 2

Solution:

$\int^{2}_{1.5}f \left(x\right)dx,$ where $f \left(x\right)=\frac{x}{2}$
$\int^{2}_{1.5}\frac{x}{2} dx =\frac{1}{2}.\int^{2}_{1.5}xdx=\frac{1}{2}\left[\frac{x^{2}}{2}\right]^{^{^2}}_{_{_{_{1.5}}}}$
$=\frac{1}{4}\left[4-2.25\right]=\frac{1}{4}\times\left[1.75\right]=\frac{175}{400}=\frac{7}{16}$