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Quiz5_Solutions - C hapler 7 M ultivariate robability...

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Chapler 7 Multivariate Probability Distributions Figure 7.6 The joint density function for Example 7.5 [email protected]): /_1o,,,x2)dx1: 1,,'r,,n*,:11*1),',,,:}(t -,1) 0 < x2 < I The question refers to the marginal behavior of d. Thus, it is necessary to find It follows directly that P(0.2 < X2 = 0.4) : :1{lno_ (0.4)3.1 t ro.zr3l\ 2LL- 3l-Lo'- ,li : 0.272 Note that the marginal density ofX2 graphs as a function that is high at x2 : 0 anc then tendsto 0 as x2 tends to 1. Does this agree with your intuition after lookin_= at Figure 7.5? Recall that in the bivariate discrete casethe conditional probabilities for X1 for , givenX2 were found by fixing attentionon the particular row in which X2: .t:; and then looking at the relative probabilities within that row. Thbt is, the indiviC- ual cell probabilities were divided by the marginal total for that row in order t: obtain conditional probabilities. I"'1(r - '])a" ::(,, *)1,,
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