Chapter 3. Multivariate Distributions.

3-1 Chapter 3. Multivariate of the most interesting problems in statistics involve looking at more than a single measurementat a time, at relationships among measurements and comparisons between them. In order to permit us toaddress such problems, indeed to even formulate them properly, we will need to enlarge our mathematicalstructure to includemultivariate distributions,the probability distributions of pairs of random variables,triplets of random variables, and so forth. We will begin with the simplest such situation, that of pairs ofrandom variables orbivariate distributions,where we will already encounter most of the key Discrete Bivariate two random variables defined on the same sample spaceS; that is, defined in referenceto the same experiment, so that it is both meaningful and potentially interesting to consider how they mayinteract or affect one another, we will define theirbivariate probability functionbyp(x, y) =P(X=xandY=y).( )In a direct analogy to the case of a single random variable (theunivariatecase),p(x, y) may be thought ofas describing the distribution of a unit mass in the (x, y) plane, withp(x, y) representing the mass assignedto the point (x, y), considered as a spike at (x, y) of heightp(x, y).

3-1 Chapter 3. Multivariate Distributions. ... structure to include multivariate distributions, the probability distributions of pairs of random variables, triplets of random variables, and so forth. We will begin with the simplest such situation, that of pairs of ... describes a surface in 3-dimensional space, and the probability that (X;Y) ...

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  Chapter, Distribution, Chapter 3, Probability, Multivariate, Multivariate distributions

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