What is the probability density function of t

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Reference no: EM131469773

Question: For the equipment mentioned in Problem,

a. Derive the failure rate function r(t), and draw a graph of the function.

b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year.

c. Does r(20) accurately estimate your answer to part (b)? Why or why not?

Problem: 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?

Reference no: EM131469773

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