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Homework Statement
The number of years that a washing machine functions is a random variable whose hazard rate function, h(t), is given by
- 0.2 if 0 < t < 2
- 0.2 + 0.3(t - 2) if 2 <= t <= 5
- 1.1 if t > 5
If the washing machine is still working six years after being purchased, what is the conditional probability that it will fail within the succeeding two years?
The attempt at a solution
My interpretation of h(t) is that it is the probability that the washing machine will fail given that it has worked for t years.
The answer to the problem, I reckon, is the sum of h(6 + t) as t varies from 0 to 2. Since 6 + t > 5, then h(6 + t) = 1.1 by the def. of h. Integrating, I get 2.2. This must be wrong since probabilities are <= 1. Where did I go wrong?
The number of years that a washing machine functions is a random variable whose hazard rate function, h(t), is given by
- 0.2 if 0 < t < 2
- 0.2 + 0.3(t - 2) if 2 <= t <= 5
- 1.1 if t > 5
If the washing machine is still working six years after being purchased, what is the conditional probability that it will fail within the succeeding two years?
The attempt at a solution
My interpretation of h(t) is that it is the probability that the washing machine will fail given that it has worked for t years.
The answer to the problem, I reckon, is the sum of h(6 + t) as t varies from 0 to 2. Since 6 + t > 5, then h(6 + t) = 1.1 by the def. of h. Integrating, I get 2.2. This must be wrong since probabilities are <= 1. Where did I go wrong?