The exponential distribution is:
![\lambda e^{- \lambda x}](https://tex.z-dn.net/?f=%5Clambda%20e%5E%7B-%20%5Clambda%20x%7D)
where
![\lambda = \frac{1}{mean}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B1%7D%7Bmean%7D%3D%5Cfrac%7B1%7D%7B5%7D)
The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.
![P(A|B) = \frac{P(A and B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%7CB%29%20%3D%20%5Cfrac%7BP%28A%20and%20B%29%7D%7BP%28B%29%7D%20)
where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:
![P(x \ \textgreater \ N) = \int_N^{\infty} \frac{1}{5} e^{-x/5} dx = e^{-N/5}](https://tex.z-dn.net/?f=P%28x%20%5C%20%5Ctextgreater%20%5C%20N%29%20%3D%20%5Cint_N%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7B5%7D%20e%5E%7B-x%2F5%7D%20dx%20%3D%20e%5E%7B-N%2F5%7D%20)
Sub into conditional probability formula:
![P(x \ \textgreater \ 8 | x\ \textgreater \ 5) = \frac{P(x\ \textgreater \ 8)}{P(x\ \textgreater \ 5)} = \frac{e^{-8/5}}{e^{-5/5}} = e^{-3/5} = 0.549](https://tex.z-dn.net/?f=P%28x%20%5C%20%5Ctextgreater%20%5C%208%20%7C%20x%5C%20%5Ctextgreater%20%5C%205%29%20%3D%20%5Cfrac%7BP%28x%5C%20%5Ctextgreater%20%5C%208%29%7D%7BP%28x%5C%20%5Ctextgreater%20%5C%205%29%7D%20%3D%20%5Cfrac%7Be%5E%7B-8%2F5%7D%7D%7Be%5E%7B-5%2F5%7D%7D%20%3D%20e%5E%7B-3%2F5%7D%20%3D%200.549)
Final Answer: Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%
Answer:
it would be a distance of 7 units
Step-by-step explanation:
Answer:
4320
Step-by-step explanation:
multiply 6% by 18(One year/12 months + Half of a year/6) you will get 1.08. Then take that and multiply that by 4000. You should get 4320
Answer:
15.9973389992
Step-by-step explanation:
Simplify the square roots and use exact decimals
(7 + 2.2360679775) Add inside the parentheses
1.73205080757 (9.2360679775) Multiply
15.9973389992
If this answer is correct, please make me Brainliest!
Answer:
-78
Step-by-step explanation:
We subtract 1, then 3, then 5, then 7
Then subtract 9,11,13,15,17
-21 -11 = -33
-33 -13 = -46
-46 -15 = -61
-61 -17 = -78
3, 2, -1, -6, -13, -22, -33, -46, -61, -78