Question

Suppose E(Z)=7 and E[Z(Z-1)]=200. Find V(Z).

Answer 1

Please define V(Z) in terms of expected values.

Answer 2

V(Z)=E[(Z-u)^2]

Answer 3

Very good. Now expand that expression inside the Expected Value brackets.

Answer 4

\[\sum_{}^{}(Z-u)^2p(z)\]

Answer 5

What is that? \(E\left[(Z-\mu)^{2}\right] = E\left[Z^{2} - 2Z\mu + \mu^{2}\right]\) That is what "expand inside the ... brackets" means. Now what?

Answer 6

the summation is how you find an Expected value (E())

Answer 7

sorry i had misread what you typed

Answer 8

I don't know what to do from here

Answer 9

You should have rules for linear combinations of expected values:

\(E\left[Z^{2} - 2Z\mu + \mu^{2}\right] = E\left[Z^{2}\right] -2\mu E\left[Z\right] + \mu^{2}\)

Does that look plausible?

Answer 10

yeah okay.

Answer 11

so how do I find E[Z^2] and mu? I can replace E[Z] with the value given...

Answer 12

Given in the problem statement. Keep in mind that \(E[Z] = \mu\)

Answer 13

duh... i'm an idiot. and E[Z^2]?

Answer 14

You are SO CLOSE!!

E[Z]=7
E[Z(Z-1)]=200

E[Z(Z-1)] = E[Z^2 - Z] = E[Z^2] - E[Z] = E[Z^2] - 7 = 200

Answer 15

ohhhh so 207=E[z^2]!

Answer 16

then its just adding and multiplying!

Answer 17

That easy, once you see all the pieces!!

Answer 18

Thanks so much!