20 Joint Dist, Cov, Corr

20 Joint Dist, Cov, Corr - Joint Distributions Covariance...

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Click to edit Master subtitle style 9/7/10 Joint Distributions, Covariance and Correlation April 16

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9/7/10 Example Consider the following continuous joint density function: fXY(x,y) = k(6 - x - y) for 0<x<2 and 2<y<4 a) Find k. We seek k such that the volume under the surface defined by fXY(x,y) over the region 0<x<2 and 2<y<4 is equal to one. b) Find P(x<1 and y<3)
9/7/10 c) Find P(X+Y < 4) First we must determine the region and integration limits:

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9/7/10 Example, cont. d) Find the marginal distributions of X and Y e) Find P(X<1.5) We can find this from the marginal density of X
9/7/10 Example, cont. f) Find the conditional distribution fX| y(X|Y=3) Conditional is the joint over the marginal. Also note that Y=3

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9/7/10 Example, cont. In this case the domain of x is the same as in the joint density. In some cases, this will not be true. Suppose the region in the (x,y) plane over which the density is defined is:
Conditional Expectation We have learned already the definition of expected value: E(X) = x fX(x) dx where Rx tells us to integrate over the domain of x. Rx

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20 Joint Dist, Cov, Corr - Joint Distributions Covariance...

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