The document discusses a random variable x with a cumulative distribution function fx and introduces another random variable y defined as y=exp(2x+1). It outlines the process to find the cumulative distribution function of y in terms of the cdf of x. The solution involves expressing the relationship between these variables across the entire real axis.

1. Consider a random variable X with a cumulative distribution function Fx. Let the random
variable Y=exp(2X+1). Find the cumulative distribution function of Y, expressed it in terms of
the CDF of X. Define it on the whole real axis.
Solution
G(x) = P(Y