Transcription of Reading 7a: Joint Distributions, Independence
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Reading 7a: Joint Distributions, Independence
Joint Distributions, IndependenceClass 7, Orloff and Jonathan Bloom1 Learning Goals1. Understand what is meant by ajointpmf, pdf and cdf of two random Be able to compute probabilities and marginals from a Joint pmf or Be able to test whether two random variables are IntroductionIn science and in real life, we are often interested in two (or more) random variables at thesame time. For example, we might measure the height and weight of giraffes, or the IQand birthweight of children, or the frequency of exercise and the rate of heart disease inadults, or the level of air pollution and rate of respiratory illness in cities, or the number ofFacebook friends and the age of Facebook :What relationship would you expect in each of the five examples above?
The event A is just the upper-left-hand quadrant. Because the density is not constant we must compute an integral to nd the probability. P(A) = Z:5 Z 1 :5 :5 1 3x 4xydydx = Z dx: 0 2xy2 = 5:5 0 Z 0. 2 dx = 3 16: 3.4 Joint cumulative distribution function. Suppose X and Y are jointly-distributed random variables. We will use the notation ‘X
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