STAT330 Lecture Notes - Lecture 10: Moment-Generating Function, Multivariate Random Variable, Whta

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Reza

Document Summary

Last class: properties of the moment generating function, linear transformations, uniqueness of the m. g. f. Today: an example about , joint probability distributions. Consider x n( , assume that (but show it later) Most studies collect information on multiple variables per subject rather than one variable. For example: in a health-related study, the height x1, weight x2, blood pressure x3 and temperature x4 of the subjects are collected. The data per subject is a random vector y = (y1, y2, y3, y4). Even if we collect one variable of interest, say x : the height of an individual, we usually observe x on a sample of n randomly selected subjects, i. e. x1, . , xn, where xi shows, in this example, the height of the i th person in the sampe. Xn are independent (not a ecting each others" values), and we are interested in the joint distribution of the n random variables.