Question

Stats: Am I on the right path?

The problem is, "Show that the variance of the finite population (c_1,...c_N) can be written as ...

Answer 1

\[\sigma ^{2} = \frac{ { \sum_{i=1}^{N} }{ }c_i ^{2} }{ N } -\mu ^{2}\]

Answer 2

So, my thought thus far has been, start with the formula for sigma^2\[\sigma ^{2} = \frac{ 1 }{ N } \sum_{i=1}^{N} (c_i-\mu)^{2}\] and then use the formula for mu instead of just the symbol for it.

Answer 3

ok, those must be equally likely events to be able to use that formula ... ?

Answer 4

its a weird varaition of it in my book, gimme 2 secs, ill take a picture.

Answer 5

Its problem 8.15. I assume this is just using the formulae for mu and sigma^2 and shuffling things around until it looks like that, but I was wondering if I could get some confirmation of that before I spend an hour on a fruitless pursuit

Answer 6

yeah, the end result is correct, and use
\(\large \mu =\dfrac{1}{N}\sum \limits_{i=1}^Nx_i\)

Answer 7

Ok perfect, Im probably about halfway through it, but I move frustratingly slow and wanted to make sure that was the right idea. Thanks!

Answer 8

thank wiki though :P
http://en.wikipedia.org/wiki/Variance

Answer 9

i got the answer in 2 steps,
\(\large= ...-2\mu \times \mu+\mu^2\ \\ \large = ...-\mu^2\)
last steps....