HW1 - (c Evaluate the cumulative distribution function(cdf...

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ECE4110 Homework 1 Fall 09 Cornell University T.L. Fine This assignment is to be handed in at the end of class on Thursday, 3 September. 1. (a) Describe the ranges (sets of possible values) of the random variables { X t ,t T } and the index set T for the random process that models the number X t of cars that have passed a given point on a highway by time t . (b) Repeat for the random process that models the Dow Jones Index (see attached information sheet). 2. Consider the probability space , A ,P ) where Ω = [0 , 1] ,P (( a,b )) = b - a for 0 a b 1 , the index set T = [0 , ), and the random process X T deﬁned by X T ( ω,t ) = ω 2 t 2 . (a) On the same graph, sketch the three sample functions for ω = 0 ,. 2 , 1. (b) For t = 0 . 5, evaluate the probability that the random process has amplitude less than 0.1.
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Unformatted text preview: (c) Evaluate the cumulative distribution function (cdf) F X t ( x ). (d) Evaluate the probability density function (pdf) f X t ( x ). 3.-6. Please work the following problems from the text: 7.1, 7.2, 7.3, 7.6a 7. Based upon information provided in Chapters 4 and 6 of the text and the usage that X ∼ Z is read as “the random variable X is distributed according to the probability law Z ”, write out the probability mass functions (pmfs) or the pdfs and the associated mean or expected values EX for each of the following cases: X ∼ U ( a,b ) , X ∼ B ( n,p ) , X ∼ E ( α ) , X ∼ P ( λ ) , X ∼ L ( α ) , X ∼ N ( m,σ 2 ) . 1...
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