When transitioning from X to Y, it's important to note that the PDF of the resultant function can be evaluated directly from X. Using the Distribution Function Technique, you first find the CDF as F_Y(y)=P(Y <= y), and then differentiate it to get the PDF.
Alternatively, you can use the Change-of-Variable Technique that varies based on if the function f(X) is increasing or decreasing; the resultant math can be found at https://newonlinecourses.science.psu.edu/stat414/node/157//
When transitioning from X to Y, it's important to note that the PDF of the resultant function can be evaluated directly from X. Using the Distribution Function Technique, you first find the CDF as F_Y(y)=P(Y <= y), and then differentiate it to get the PDF.
Alternatively, you can use the Change-of-Variable Technique that varies based on if the function f(X) is increasing or decreasing; the resultant math can be found at https://newonlinecourses.science.psu.edu/stat414/node/157//