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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A piece of equipment has a lifetime T (measured in years) that is a continuous random variable with cumulative distribution
F(t) = 1 - e-t/10 - (t/10) e-t/10 for all t ≥ 0.
a. What is the
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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