it is sometimes useful to consider the moment generating function of random variable this is the function defined by (se sx moment generating function ( the moment generating functions of two random variables coincide if and only if the random variables have the same distributionsee also theorem example (moment generation function of the gamma(aldistributionlet gamma(alfor lthe moment generating function of at is given by (see sx -lx la xa- dx (   -( - ) ( ) xa- dx - (al- { sx pdf of gamma( , -sfor lm(sinterestinglythe moment generating function has much simpler formula than the pdf joint distributions distributions for random vectors and stochastic processes can be specified in much the same way as for random variables in particularthe distribution of random vector [ xn ]is completely determined by specifying the joint cdf fdefined by joint cdf ( xn [ xn xn ]xi ri similarlythe distribution of stochastic processthat isa collection of random variables {xt }for some index set is completely determined by its finite-dimensional distributionsspecificallythe distributions of the random vectors [xt xtn ]for every choice of and tn by analogy to the one-dimensional casea random vector [ xn ]taking values in rn is said to have pdf ifin the continuous casez [ bf (xdx( stochastic process for all -dimensional rectangles replace the integral with sum for the discrete case the pdf is also called the joint pdf of xn the pdfs of the individual components -called marginal pdfs -can be recovered from the joint pdf by "integrating out the other variablesfor examplefor continuous random vector [xy]with pdf the pdf fx of is given by fx (xf (xydy joint pdf marginal pdf