problems3

# problems3 - 1 Problems set 3 ENGRD 2700 Due Wednesday July...

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1 Problems set 3; ENGRD 2700 Due Wednesday, July 17 during the lecture. By that day, we should be done with Chapters 5, 6 and 7. The material that I will see during this week is on those chapters, but that doesn’t mean is all that material. Regard the book as a good reference for examples and problems, but it should be enough with the lecture notes. 1. The convolution formula given in class last Monday was as follows: Given X 1 and X 2 independent random variables with densities f 1 ( x ) and f 2 ( x ), the density of X 1 + X 2 is f ( x ) = f 1 * f 2 ( x ) computed as f ( x ) = f 1 * f 2 ( x ) = Z -∞ f 1 ( x - y ) f 2 ( y ) dy,x R . If X 1 0 and X 2 0 the integral runs from 0 to . (a) Suppose X 1 and X 2 are iidrv each with N (0 , 1) density. Show that X 1 + X 2 has N (0 2 = 2) density. Hint: You will have to complete a square in the integral. (b) Suppose X 1 ,X 2 ,X 3 are iidrv each with exp ( λ ), λ > 0. What is the density of X 1 + X 2 + X 3 ? Hint: X 1 + X

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## This note was uploaded on 09/09/2008 for the course ENGRD 2700 taught by Professor Staff during the Summer '05 term at Cornell.

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problems3 - 1 Problems set 3 ENGRD 2700 Due Wednesday July...

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