The problem involves continuous random variables, specifically defining a probability density function for variable X and deriving the cumulative distribution function for variable Y, which is defined as Y=X^2. The discussion centers around understanding the relationship between the two variables and the implications of their definitions.
Participants have provided insights into the formulation of G(y) and have identified different cases based on the value of y. There is acknowledgment of the need to integrate the probability density function, and while some clarity has been achieved, there remains uncertainty regarding the domain for one of the cases.
Participants are navigating the definitions and relationships between the random variables, particularly the implications of squaring X to define Y. There is a noted concern about the correctness of the domain for the integration in one of the cases.
gerben said:G(y), the cummulative probability distribution function of Y, is a function that gives the probability that Y is smaller than y.
P(-sqrt(Y)<=X<=sqrt(Y)) is a way of writing: Probability that X is in between plus and minus the square root of Y (note the use of capital Y here, y and Y are not the same thing).
gerben said:yes exactly