00:01
Hi, i'm david and i'm here to have you answering your question.
00:03
Now let me bring up your question here.
00:06
Now in this question we will discuss about the exponential distribution.
00:10
Now we're supposed that the mtpm for new automated manufacturing follow exponential distribution.
00:20
So i'll recall you that, let's follow the exponential with the mean lambda it will equal to and then it will have the density fx equal to 1 over lambda e to the minus lambda x.
00:40
Now because x in this question follow the exponential with the mean equal to the 12 .2 so therefore the density of the x equal to 1 over 12 .2 e to the minus 12 .2 x for the x squared equal to 0 .2.
01:02
Now in the part i want to find the probability that it will be more than 17 hours.
01:12
So x greater than 17 hours.
01:16
So this one should the integral from 17 to infinity.
01:22
Of the fx will be 1 over 12 .2, e .e to the minus 12 .2 x dx.
01:31
And the entire derivative of this one, it will equal to the minus e.
01:35
The power minus 12 .2 x from 17 to infinity and if we compute the answer and the infinity got the 0 and under 17 we have equal to each the power minus uh sorry this one i make a mistake here so this one should be the one over lambda here minus one over lambda x so this one should be one over side by that so this one will be one over 12 .2 doesn't also one over so one over 12 .2 minus 1 over 12 .2 so have we have here will be 17 over 12 .2 if we compute this value 17 divided by 12 .2 and then the to the power on that, get equal to 0 .2, 4, 8...