The two random variables $X$ and $Y$ are converted by $Y=g(X)$ as shown in the following equation. Find the probability density function of the random variable $Y$ when the probability density function of the random variable $X$ has a uniform distribution as follows.
Problem and solution:
If you see the solution of this problem, you can find out $p_Y(y) = 1/(8*\sqrt{y}) + δ(y)/2$. But I just can't understand why there's an $δ(y)/2$ in $p_Y(y)$. Could you tell me why $δ(y)/2$ is added to $1/(8*\sqrt{y})$? I've been trying to understand for three days, but I can't figure it out.