00:01
Hi, i'm david and i'm here to have you answer your question.
00:04
Now let me bring up your question here.
00:07
In this question we talk about the exponential distribution.
00:10
Here particularly we have the x, it will follow by, it is the lifetime of the component, and then x followed by the exponential with the mean equal to 1 ,900 and we have the dense of the fx equal to 1 over 1 ,900 each the power minus x over 1 ,900 for the x greater than 0.
00:44
Now in the part i am the question when you find the probability that a component lasts more than 650, so x greater than 650.
00:55
Now this one just equal to the integral from single 50 to infinity.
01:01
Then we have 1 over 1 ,900 e to the power minus x over 1 ,900 d x.
01:09
And then we get equal to untidy derivative equal to minus e to the power minus x over 1 ,900.
01:17
E value it from 650 to the infinity.
01:21
If we put the infinity inside, we got the 0, and we put the 650 inside, we have the plus e to the power minus 650.
01:29
650 over 19000 then we do the calculation each the power of minus 650 defined you by 1900 we get equal to the 0 .7103 that's going to be the answer for the part a now for the part b the number of the hour by which 18 % of own components have found so once you find the probability that the 18 % percent of the the component will fail means that x it will be greater than some number a here, such that this one will equal to the 18%.
02:12
And then to find this probability, we know that 0 .18 % will be equal to 0 .18...