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?
13) Consider the checkerboard arrangement shown below. Assume that the red checker can move diagonally
upward, one square at a time, on the white squares. It may not enter a square if occupied by another checker, but
may jump over it. How many routes are there for the red checker to the top of the board?
12) The prime factors of 1365 are 3, 5, 7 and 13. Determine the total number of divisors of 1365.
11) What is the sum of numbers in row #8 of Pascal's Triangle?
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