ECE280_SS20_HW03.pdf - ECE280 Electrical Engineering...

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ECE280 Electrical Engineering Analysis:Engineering Probability and Statistics, Spring 2020, MSU Homework Assignment 3, Due on 04/13/2020, Monday at 11:59 pm electronically to D2L Problem 1. Let X and Y be two jointly distributed continuous random variables representing voltages measured in Volts at two different nodes of a circuit. X has the marginal density function: g ( x ) = ( 2 x +1 2 , 0 x 1 0 , otherwise (1) You are also given the conditional density function: f Y ( y | x ) = ( 2( x + y ) 2 x +1 , 0 x 1 and 0 y 1 0 , otherwise (2) (a) Compute P ( Y 0 . 5 | X = 0 . 5) the probability that Y is less than or equal to 0 . 5 given that we know X = 0 . 5. (b) Compute the probability that the voltage X is in the range 1 4 X 1 2 and the voltage Y is less than 1/2 at the same time. In other words compute the probability P ( 1 4 X 1 2 , Y 1 2 ). (c) Compute the covariance of X and Y . Problem 2. A game consists of rolling a pair of dice, one red and one blue. Let X denote the outcome of the red dice and let Y denote the outcome of the blue dice. X and Y are independent

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