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a) Determine the value of k. (b) Determine the cdf. (c) Calculate the probability that time to failure is between 2 and 6 years.

a) Determine the value of k. (b) Determine the cdf. (c) Calculate the probability that time to failure is between 2 and 6 years.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Let X denote the time to failure (in years) of a certain engineering component. Suppose the pdf of X is f(x) =k/(x+4)^3 for x≥0.

a) Determine the value of k.

(b) Determine the cdf.

(c) Calculate the probability that time to failure is between 2 and 6 years.

(d) If the component has a salvage value equal to 100/(4+x)when its time to failure is x, what is the expected salvage value?

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