I'm learning basic probability and have some understanding of PDF's and CDF's now. (I've not done expected values yet though so I'm not familiar with that notation). I've come across standardization of a random variable, X, which then gives a new random variable Y with the properties that Y has zero mean and unit variance (and therefore unit standard deviation). My first question is, does X have to have a normal distribution? I've seen this stated explicitly in some texts but not in others. My second question is, what is the benefit of defining a new random variable instead of just using our old one? Can anyone give a clear intuitive example of when you may want to standardize data but also when you may not want to standardize data? I'm guessing it involves wanting to compare different data from different sample spaces maybe? EDIT: Or does it involve comparing data on the same sample space but in vastly different regions of the sample space (i.e one data set involves X looking at temperatures between 0 and 5 degrees whilst another data set looks at temps between 150 and 170 degrees)?