00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here we are going to discuss about the exponential distribution.
00:11
Let me remind you that if the x that followed by exponential, when the mean equal to the petal, and then the density of the x equals to 1 over petal e to the power minus x over the petal for the x -queter equal to the 0.
00:28
In the question here we have the time between the 1st, arrivals of the customers x will follow by exponential when the beta equal to the 0 .43.
00:40
And therefore we can find the density of the x equal to 1 over 0 .43, e to the power minus x over the 0 .43.
00:52
And x squared equal to the 0.
00:54
So notice that the time here will be in the minute.
00:59
And in the question, i want to find the probability that the time here will be less than the 15 seconds.
01:08
We know 15 seconds will be the 15 divided by 60.
01:11
It will equal to the 0 .25 minute.
01:18
So therefore x will be smaller than the 0 .25.
01:21
This one just equal to integral, starting from 0 to the 0 to the 0.
01:25
The density will be 1 over 0 .0 .043, e to the power minus x over the 0 .43, the x.
01:35
Anti -derivative will be the minus e to the power minus x over the 0 .43, evaluating from the 0 -1 to the 0 .25.
01:45
If we plug, we get equal to 1 minus 0 .0, e to the power of the minus 0 .25 over the 0 .40.
01:55
So if we compute it, we have the minus 0 .25, the vanymed 0 .43, e to the power of the answer, 1 minus the answer.
02:05
It will equal to the 0 .44.
02:10
I need to round the answer to 2 decimal places.
02:15
And that will be the answer for the first question a...