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Assignment3 - pulses/hr(b To make computations simpler you...

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1 Assignment 3, STAT220-Winter 2011 Instructor: Kamyar Moshksar Due on Monday, Feb. 28th Problem 1 - Let X Bi(10 , 0 . 1) and Y Bi(5 , 0 . 2) be two independent random variables defined on similar sample spaces. Find P(X < Y) and P(X > Y | Y 2) . Problem 2- Let X and Y be two independent uniform random variables defined on the same sample space such that range(X) = {- 1 , 0 , 1 } and range(Y) = { 1 , 2 , 3 } . Find and sketch the c . d . f . of the random variable 2X - Y . Problem 3- Suppose that the number of pulses arriving at a Geiger counter in one hour period is a Poisson r.v., and that in any one hour time period there is a 13.53 chance that no pulses arrive. (a) Show that the average number of pulses arriving per hour is approximately
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Unformatted text preview: pulses/hr. (b) To make computations simpler, you may use the approximation λ = 2 . What is the probability that two or more pulses arrive between 6 pm and 7pm on a given day? Problem 4-(a)-Show that the function F : R → R defined by F ( x ) = exp(-exp(-x )) for any x ∈ R is a c . d . f . . (b) Assume X is a random variable whose c . d . f . is F ( . ) . Compute P( X > 3 | X 2 ≤ 25) . Problem 5-Let X be a poisson random variable with parameter λ , i.e., f X ( x ) = exp(-λ ) λ-x x ! for x ∈ N ∪ { } . Write a computer code to calculate lim λ →∞ P(X ≤ λ ) . What is your answer?...
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