anyone happen to have the proof of the Variance for Binomial Distribution?

[UncleWai]

My schedule is packed and I am forced to do this PITA statistic assignment late in the night.

We have to prove the E(x) and Var(x) for 7 different distributions.

I am stucked on the binomial distribution, i got the E(x).
I was told to use Var(x) = E(X (X-1)) + E(x) - E^2(X)

But I just don't see how that can become np(1-p).

Anyone happen to see the proof somewhere?

 

[Random Variable]

Did you get the moment-generating function for the binomial distribution?

 

[Random Variable]

then it's just the second derivative of the moment-generating functione evaluated at 0 minus the square of the first derivative of the MGF evaluated at zero

 

[silverpig]

Google is your friend.

Sort of what you're looking for?

 

[MrX82]

you can always prove it by indicator variables.

a bin(n,p) r.v. is the sum of n iid bernouli p variables.

 

[UncleWai]

Originally posted by: Random Variable
Did you get the moment-generating function for the binomial distribution?

I think we are slow, we haven't learned MGF yet.

We have to prove in terms of series
Summation of xi*f(xi)

then do a bunch of index switching and simplifying.

If I can make sense of the index switching with E(x(x-1)).
Plus I don't see how something + np - (np)^2 = np(1-p)