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GATE ECE 2006 | Question-52

A uniformly distributed random variable $X$ with probability density function
\[ f_{\gamma}(x)=\frac{1}{10}(t r(x+5)-u(x-5)) \]
where $u(.)$ is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable $Y$ would be


$f_{Y}(y)=\frac{1}{5}(u(y+2.5)-u(y-2.5))$
$f_{Y}(y)=0.5 \delta(y)+0.5 \delta(y-1)$
$f_{Y}(y)=0.25 \delta(y+2.5)+0.25 \delta(y-2.5)$ $+0.5 \delta(y)$
$f_{Y}(y)=0.25 \delta(y+2.5)+0.25 \delta(y-2.5) +\frac{1}{10}(u(y+2.5)-u(y-2.5))$

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