homework12

homework12 - E [ L ]. c. ind the covariance COV ( L, T )....

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Probability for Engineering Applications Assignment #12, due at the beginning of class on Thursday, April 27 th , 2006 1. (4 pts) A frm sends out two types oF Faxes. The frst kind only contains text and requires 40 seconds to transmit each page. The second kind contains pictures and takes 60 seconds per page. ±axes can be 1, 2 or 3 pages long. Let the random variables L and T denote the length oF a Fax and the time to transmit a page, respectively. The joint pmF oF L and T is given by T L 40 60 1 0 . 15 0 . 10 2 0 . 30 0 . 20 3 0 . 15 0 . 10 a. ±ind the marginal pmF’s oF T and L . b. ±ind the expected values E [ T ] and
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Unformatted text preview: E [ L ]. c. ind the covariance COV ( L, T ). d. ind the correlation coecient L,T . 2. (2 pts) Consider the Following joint pdF f X,Y ( x, y ) = ( e-2 | y-x 2 |-x- < y < , x else ind E [ Y | X = x ]. 3. (4 pts) The random variables Y 1 , Y 2 , Y 3 and Y 4 have the joint PD f Y 1 ,Y 2 ,Y 3 ,Y 4 ( y 1 , y 2 , y 3 , y 4 ) = ( 4 y 1 y 2 1 , y 3 y 4 1 else a. ind the marginal pdF f Y 2 ,Y 3 ( y 2 , y 3 ). b. ind the marginal pdF f Y 3 ( y 3 ). 1...
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