ORIE 360/560 Fall 2007Assignment 6Due Tuesday, Oct. 16 at 2:00 pmPlease remember to show your work!Please remember to put your section number and net id on theassignment!Problem 1.SupposeXhas an exponential distribution, and thatP[X > .01] = 1/2.Find the uniquenumbertsatisfyingP[X > t] =.9.Problem 2.IfXhas densityfX(x) =12λe-λ|x|, forx∈R, thenXis said to have thedouble exponentialdistribution with parameterλ. Find the mean and variance of such a random variable.Hint: you could usemoment generating functions, although it’s not required.Problem 3.Find the moment generating function of the binomial(n, p) random variable, wheren≥1 and0< p <1. Use the result to check the values for the mean and variance given in class (or in the text).Problem 4.A contractor purchases a shipment of 100 widgets, 20 of which are defective.(a) If the contractor tests the widgets one by one, what is the probability that the first defective widget willbe discovered on the 15th trial?
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