"A first Course in probability"-chaper5-continuous random variable-random variable function distribution

In discussing the distribution of continuous random variable functions, we can get a simplified version of the model from the general situation (as discussed in the article on normal distribution).

Recall the process of solving the function distribution of random variables using the relationship between distribution function and probability density, there is y=g (x), if G (x) is strictly monotonous, then we can use the inverse function to get the range of x directly (if it is not monotonous, need to consider a little more), Thus, the distribution function of Y and the distribution function of X are established, and the specific form of the theorem is as follows:

"A first Course in probability"-chaper5-continuous random variable-random variable function distribution