Answer:
Follows are the solution to the given points:
Step-by-step explanation:
Given value:
For point a:
Moment generating function of X=?
Using formula:
integrating the values by parts:
![u = x \\\\dv = e^{(t-1)x}\\\\dx =dx \\\\v= \frac{e^{(t-1)x}}{t-1}\\\\M(t) =[\frac{e^{(t-1)x}}{t-1}]^{-\infty}_{0} -\int^{\infty}_{0} \frac{e^{(t-1)x}}{t-1} \ dx\\\\](https://tex.z-dn.net/?f=u%20%3D%20x%20%5C%5C%5C%5Cdv%20%3D%20e%5E%7B%28t-1%29x%7D%5C%5C%5C%5Cdx%20%3Ddx%20%5C%5C%5C%5Cv%3D%20%5Cfrac%7Be%5E%7B%28t-1%29x%7D%7D%7Bt-1%7D%5C%5C%5C%5CM%28t%29%20%3D%5B%5Cfrac%7Be%5E%7B%28t-1%29x%7D%7D%7Bt-1%7D%5D%5E%7B-%5Cinfty%7D_%7B0%7D%20%20-%5Cint%5E%7B%5Cinfty%7D_%7B0%7D%20%5Cfrac%7Be%5E%7B%28t-1%29x%7D%7D%7Bt-1%7D%20%5C%20dx%5C%5C%5C%5C)
![= \frac{1}{t-1} (0) - [\frac{e^{(t-1)x}}{(t-1)^2}]^{\infty}_{0}\\\\=\frac{1}{(t-1)^2}(0-1)\\\\=\frac{1}{(t-1)^2}\\\\](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7Bt-1%7D%20%280%29%20-%20%5B%5Cfrac%7Be%5E%7B%28t-1%29x%7D%7D%7B%28t-1%29%5E2%7D%5D%5E%7B%5Cinfty%7D_%7B0%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B%28t-1%29%5E2%7D%280-1%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B%28t-1%29%5E2%7D%5C%5C%5C%5C)
Therefore, the moment value generating by the function is 
In point b:
Using formula:
form point (a):
Differentiating the value with respect of t
when 
The equation computed shows that the number of minutes that it will take to process fifteen passengers is 11.11 minutes.
<h3>How to solve the equation</h3>
Since Katrina averages fifteen passengers every twenty minutes and Stefon also works for the airline and averages fifteen passengers every twenty-five minutes, this can be represented this:
1/x = 1/20 + 1/25
1/x = 9/100
9x = 100
Divide through by 9
x = 100/9
x = 11.11 minutes
Learn more about equations on:
brainly.com/question/1214333
260.
Subtract the nth number from the (n+1)st. You get 2, 4, 8, 14, ?
Do it again for that sequence. You get 2, 4, 6, ?
Maybe that sequence is 2, 4, 6, 8, 10, 12, 14, 16, 18, ...
If so, then the sequence "above" it is 2, 4, 8, 14, 22, 32, 44, 58, 74, ...
And the original sequence is 2, 4, 8, 16, 30, 52, 84, 128, 186, 260, ...
