Please show steps of these probabilityquestions:
1. Let X ~ N (0, sigma^2). Calculate the density of Y=X^3
2. Let X ~ exp (1) and Y|X = x ~ uniform (0,x). Find p(X,Y).
See attached file for better symbol representation.
This solution shows step-by-step calculations of the probability theory questions by determining the density of Y=X^3 by using the distribution function using integration and also finding p(X,Y) using the exponential distribution. An annotated diagram is included for further topic understanding.