Problem #10: The velocity of a particle in a gas is a random variable $X$ with probability distribution $$ f_{X} (x)=4 X^{2} ^{-2x} \quad x>0 $$ The kinetic energy of the particle is $Y=\frac{1}{2} m X^{2} $ Suppose that the mass of the particle is $25 \mathrm{yg} $. Find the probability distribution of $y$. (Do not convert any units.) Problem #10: Enter your answer as a symbolic function of $y$, as in these examples SP.VS. 886