Let Y = max(X, 0), where X is a random variable. This is an example of a transformation that takes the maximum of the original random variable and 0 solve and find pdf of y
To find the probability density function (pdf) of Y, we need to consider the possible values that Y can take on.
Since Y = max(X, 0), the possible values of Y will be all non-negative values. If X is non-negative, then Y = X. If X is negative, then Y = 0. Therefore, the pdf of Y will be:
fY(y) = fX(y) if y ≥ 0
fY(y) = 0 if y < 0
where fX(y) is the pdf of X.
So, we can find the pdf of Y by using the pdf of X and considering the two cases above.