Some Important Theorems for Distribution Functions

Change of Variable. If P x) is a distribution function in the variable x and X = f y), then the corresponding distribution function in y will be 

Independent Distributions. If xi,. . ., Xn constitute a set of n independent variables each with an independent distribution function then the joint distribution fimction for the set of variables is the product of the individual distribution functions  

Linear Combinations. If the quantity y is taken as some linear combination of the independently distributed variables (xi, X2,. . , Xn), that is, 

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