# hw#2a - MS&E 4040 Fall 2011 - HW #2 1. Consider a skewed...

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1. Consider a skewed uniform distribution function deﬁned as p u ( x | x 0 ,a,m ) = 0 if x < x 0 - a 1 2 a [1 - m ( x - x 0 )] if x 0 - a x x 0 + a 0 if x > x 0 + a where | m | < 1 (a) Plot the probability distribution function p ( x | x 0 ,a,m ) schematically indicating the signiﬁcant features and the relationship to the parameters x 0 , a and m . (b) Calculate analytically the ﬁrst three moments of this distribution μ , σ 2 and γ 1 (skewness). 2. Consider the exponential probability distribution function deﬁned for x > 0 given as p e ( x | τ ) = 1 τ e - x/τ (a) Show that the distribution is properly normalized and determine the cummulative distribution function P e ( x | τ ). (b) Determine analytically the ﬁrst three moments of the distribution ( μ , σ 2 and γ 1 ) in terms of the only parameter in the probability distribution function τ . (c) On Blackboard, there is a data ﬁle containing the results from a Monte Carlo run for the Wisconsin dice game with the rules of no multiple wins and the house covers all loses (

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## This note was uploaded on 09/29/2011 for the course MSE 4040 at Cornell.

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hw#2a - MS&E 4040 Fall 2011 - HW #2 1. Consider a skewed...

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