Let X = the time (in 10-1 weeks) from shipment of a defective product until the customer returns the product. Suppose that the minimum return time is y = 5.5 and that the excess X - 5.5 over the minimum has a Weibull distribution with parameters a = 2 and B = 1.5.(a) What is the cdf of X?x< 5.5F(x) = {x2 5.5(b) What are the expected return time and variance of return time? [Hint: First obtain E(X - 5.5) and V(X - 5.5).] (Round your answers to three decimal places.)E(X) =V(X) =|10-1 weeks(10-1 weeks)?(c) Compute P(X > 7). (Round your answer to four decimal places.)(d) Compute P(7 SXS 8.5). (Round your answer to four decimal places.)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, . . . , Xn be iid with pdf f(x) = 1 x √ 2πθ2 e − (log(x)−θ1) 2 2θ2 , −∞ < x < ∞, and unknown parameters θ1 and θ2. Find the maximum likelihood estimators for θ1 and θ2, respectively
Let X = the time (in 10−1 weeks) from shipment of a defective product until the customer returns the product. Suppose that the minimum return time is γ = 5.5 and that the excess X − 5.5 over the minimum has a Weibull distribution with parameters α = 2 and β = 1.5. What are the expected return time and variance of return time? [Hint: First obtain E(X − 5.5) and V(X − 5.5).]
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Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)
Let X = the time (in 10−1 weeks) from shipment of a defective product until the customer returns the product. Suppose that the minimum return time is γ = 5.5 and that the excess X − 5.5 over the minimum has a Weibull distribution with parameters α = 2 and β = 1.5. Compute P(7 ≤ X ≤ 8.5).(Round your answer to four decimal places.)
Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?
a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?

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