Answer:
A, D , and E
Step-by-step explanation:
We have that:
is the image of CD after a dilation of scale factor n.
We use the relation between the image length and object length:
Option A
If n=3/2, then
This is true.
Option B
If n=4, then
This is false.
Option C
If n=8, then
This too is false.
Option D
If n=2, then
This is true
Option E
If n=3/4, then
This is also true.
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: