A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space in
side so they can also be used to store props. How much space is inside the steps? Give an exact answer (do not round).
1 answer:
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Answer:
Step-by-step explanation:
For this case we can use the moment generating function for the normal model given by:
And this function is very useful when the distribution analyzed have exponentials and we can write the generating moment function can be write like this:
And we have that the moment generating function can be write like this:
And we can write this as an infinite series like this:
And since this series converges absolutely for all the possible values of tX as converges the series e^2, we can use this to write this expression:
and we can use the property that the convergent power series can be equal only if they are equal term by term and then we have:
And then we have this:
And then we can find the
And we can find the variance like this :
And first we find:
And then the variance is given by:
The given expression is
We have to write it in a different way and for that, we have to check the factors of 125 and x^4 .
And factors of 125 are 25 and 5.
Radical 25 equals to 5 and radical is
.
So we will get
And that's the another way to write the given expression .