A piece of equipment has a lifetime t measured in years, Engineering Mathematics

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A piece of equipment has a lifetime t measured in years

Question: A piece of equipment has a lifetime T (measured in years) that is a continuous random variable with cumulative distribution function

F(t) = 1 - e^-t/10 - (t/10) e^-t/10 for all t ≥ 0

a. What is the probability density function of T?

b. What is the probability that a piece of equipment survives more than 20 years?

c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years?

d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years?

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Engineering Mathematics: A piece of equipment has a lifetime t measured in years

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