Question

The probability density function of a random variable 'X' is given as $f_x\left(x\right)$. A random variabel Y is defined as Y = 2X. The PDF of random variable 'Y' is defined as $k{f}_x\left(\frac{y}{2}\right)$, then the value of 'k' is equal to

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

Answer 1

The correct option is C $\frac{1}{2}$

Since, $Y=2x$
Thus, $\frac{dx}{dy}=\frac{1}{2}$
$f_Y\left(y\right)=\frac{dx}{dy}{f}_x\left(x\right)=\frac{dx}{dy}{f}_x\left(\frac{y}{2}\right)$
$\therefore K=\frac{1}{2}$