Swanson plans to attempt to swim across the lake from point A to point B as shown below. To determine how far he will have to sw
im, he has chosen a point C and calculated the labeled data.
How many miles will he have to swim? Round your answer to two decimal places.
How many miles will he have to swim? Round your answer to two decimal places.
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: