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Unformatted text preview: Assignment 1 Problems: 1. A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF f P ( p ) = braceleftBigg pe p , p ∈ [0 , 1] , , otherwise . A coin produced by this machine is selected and tossed repeatedly, with successive tosses assumed independent. (a) Find the probability that a coin toss results in heads. (b) Given that a coin toss resulted in heads, find the conditional PDF of P . (c) Given that a first coin toss resulted in heads, find the conditional probability of heads on the next toss. 2. Show that for real x ( t ), we have x e ( t ) = a 2 + ∞ summationdisplay n =1 a n cos parenleftbigg 2 π n T t parenrightbigg x o ( t ) = ∞ summationdisplay n =1 b n sin parenleftbigg 2 π n T t parenrightbigg where x e ( t ) and x o ( t ) denote the even and odd parts of x ( t ), defined as x e ( t ) = x ( t ) + x (- t ) 2 x o ( t ) = x ( t )- x (- t ) 2 ....
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This note was uploaded on 11/13/2011 for the course ECEN 455 taught by Professor Staff during the Spring '08 term at Texas A&M.
- Spring '08