Let X1, X2, X3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are exponential with means 1000, 1500, and 2000. Let Y be the minimum of X1, X2, X3 and compute P(Y > 1000).
Answer to relevant QuestionsEach of eight bearings in a bearing assembly has a diameter (in millimeters) that has the pdf f(x) = 10x9, 0 < x < 1. Assuming independence, find the cdf and the pdf of the maximum diameter (say, Y) of the eight bearings and ...Let X1 and X2 be a random sample of size n = 2 from a distribution with pdf f(x) = 6x(1 − x), 0 < x < 1. Find the mean and the variance of Y = X1 + X2. The time X in minutes of a visit to a cardiovascular disease specialist by a patient is modeled by a gamma pdf with α = 1.5 and θ = 10. Suppose that you are such a patient and have four patients ahead of you. Assuming ...Let n = 9 in the T statistic defined in Equation 5.5-2. (a) Find t0.025 so that P(−t0.025 ≤ T ≤ t0.025) = 0.95. (b) Solve the inequality [−t0.025 ≤ T ≤ t0.025] so that μ is in the middle. Approximate P(39.75 ≤ X ≤ 41.25), where X is the mean of a random sample of size 32 from a distribution with mean μ = 40 and variance σ2 = 8.
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