STAT 462 Homework 7 due Thursday, November 1, 2012 1. A pdf is defined by ( 2 ) if 0 < <1 and 0 < < 2 ( , )= 0 otherwise C x y y x f x y ? ??? (a) Find the value of C . (b) Find the marginal distribution of X . (c) Find the joint cdf of X and Y . Define for all ???. 2. (a) Find P(X > Y ) if X and Y are jointly distributed with pdf , ( , )= , 0 1, 0 1. X Y f x y x ? y ? x ? ? y ? (b) Find P(X 2 < Y < X ) if X and Y are jointly distributed with pdf , ( , )=2 , 0 1, 0 1. X Y f x y x ? x ? ? y ? 3.

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STAT 462
Homework 7
due Thursday, November 1, 2012
1. A pdf is defined by
Cx (?2y) if 0 Y) if X and Y are jointly distributed with pdf
fx (,y)=x?y,0??x 1,0?y?1.
XY ,
2
(b) Find PX(

*Note: in case of marginal distributions, the marginal pdf has been provided. 1.a) From the definition of PDF we have Hence, b) Marginal distribution of X can easily be obtained by integrating the PDF over its support along the y-component...

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*Note: in case of marginal distributions, the marginal pdf has been provided. 1.a) From the definition of PDF we have Hence, b) Marginal distribution of X can easily be obtained by integrating the PDF over its support along the y-component...