Nov 13, 2020 · Generally, the fact that sometimes you talk about X living on one space (on its own) and other time on the other (joint with some Y) doesn't really matter, because in most situations, probability theory is specifically about the properties of random variables that are independent of the of the underlying spaces (although sometimes it does matter). Although the following method is more convoluted than necessary, I think it provides a fun way to see the convolution method for computing the density of a sum of independent random variables in action.

In other words, U is a uniform random variable on [0;1]. Most random number generators simulate independent copies of this random variable. Consequently, we can simulate independent random variables having distribution function F X by simulating U, a uniform random variable on [0;1], and then taking X= F 1 X (U): Example 7. Often the X variable represents the input variable or independent variable, that is, the variable being used to predict the other variable. Y often represents the output variable or the dependent variable and it is the variable being predicted. A linear correlation is when two are more variables are related linearly, i.e. A scattered plot of the data would tend to cluster

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