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Unformatted text preview: SIEO 3600 (IEOR Majors) Assignment #6 Introduction to Probability and Statistics February 24, 2010 Assignment #6 due March 2nd, 2010 ( Expectation and variance of random variables ) 1. (continued with Problem 2 in HW5) X and Y are two continuous random variables with joint probability density function f X,Y ( x,y ) = 10 xy 2 , < x < y < 1; , otherwise . (a) Compute E [ X ] and E [ Y ]. ( Hint : You have calculated the marginal PDF of X and Y in HW5) (b) Compute E [ X 2 ] and E [ Y 2 ]. (c) Use (a) and (b) to compute var( X ) and var( Y ). 2. Suppose that X and Y are independent continuous random variables. Show that (a) P ( X + Y a ) = R - F X ( a- y ) f Y ( y ) dy (b) P ( X Y ) = R - F X ( y ) f Y ( y ) dy where f Y is the density function of Y , and F X is the distribution function of X . 3. Each night different meteorologists give us the probability that it will rain the next day. To judge how well these people predict, we will score each of them as follows: If a meteorologist...
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This note was uploaded on 10/03/2011 for the course SIEO W3600 taught by Professor Yunanliu during the Spring '10 term at Columbia.
- Spring '10