The number of years that a washing machine functions is a random variable whose hazard rate function is given by λ ( t ) = { .2 0 < t < 2 .2 + .3 ( t − 2 ) 2 ≤ t < 5 1.1 t > 5 a. What is the probability that the machine will still be working 6 years after being purchased? b. If it is still working 6 years after being purchased, what is the conditional probability that it will fail within the next 2 years?
The number of years that a washing machine functions is a random variable whose hazard rate function is given by λ ( t ) = { .2 0 < t < 2 .2 + .3 ( t − 2 ) 2 ≤ t < 5 1.1 t > 5 a. What is the probability that the machine will still be working 6 years after being purchased? b. If it is still working 6 years after being purchased, what is the conditional probability that it will fail within the next 2 years?
Solution Summary: The author calculates the probability that machine would work 6 years after being purchased. The probability is 0.032.
The number of years that a washing machine functions is a random variable whose hazard rate function is given by
λ
(
t
)
=
{
.2
0
<
t
<
2
.2
+
.3
(
t
−
2
)
2
≤
t
<
5
1.1
t
>
5
a. What is the probability that the machine will still be working 6 years after being purchased?
b. If it is still working 6 years after being purchased, what is the conditional probability that it will fail within the next 2 years?
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