# hw1 - AMS 553: Homework 1 1. (L&K 4.2) Let X be a...

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AMS 553: Homework 1 X be a continuous random variable with pdf f ( x ) = x 2 + 2 3 x + 1 3 for 0 x c (a) Find the value of c ; (b) Plot the pdf f ( x ); (c) Compute and plot the cdf F ( x ); (d) Compute P ( 1 3 X 2 3 ), E [ X ], and V ar ( X ). X and Y are jointly discrete random variables with p ( x,y ) = 2 n ( n +1) for x = 1 , 2 ,...,n and y = 1 , 2 ,...,x , 0 otherwise. Compute the pmfs p X ( x ) and p Y ( y ) and determine whether X and Y are independent. X and Y are jointly continuous random variables with density function f ( x,y ) = 32 x 3 y 7 if 0 x 1 and 0 y 1, 0 otherwise. Compute f X ( x ) and f Y ( y ) and determine whether X and Y are independent. X is a discrete random variable with p X ( x ) = 0 . 25 for x = - 2 , - 1 , 1 , 2. Let Y also be a discrete random variable such that Y = X 2 . Show that Cov ( X,Y ) = 0. Therefore, uncorrelated random variables are not necessarily independent.
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## This note was uploaded on 01/31/2011 for the course AMS 553 taught by Professor Badr,h during the Spring '08 term at SUNY Stony Brook.

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