# Homework Help: The Sum Of Σ

1. Oct 22, 2005

The Sum Of....Σ

So we were given this awkward question to do out of the text book... and a classmate and I arrived at similiar answers.... for part of the question, we are supposed to right a sequence into "sum notation"

Could somebody please tell me if my notation is correct?

Say... we have a binomial random variable... X ~ binomial (n, p)

P(X ≥ k) = P(X=k) + P(X = k +1) + ...... + P(X = n)
= (nCk)(p^k)(1-p)^n-k + (nCk+1)(p^k+1)(1-p)^n-(k+1)
= "the sum of i = k to the n" (nCi)(p^i)(1-p)^n-1

I know its messy... but "the sum of i = k to the n" (nCi)(p^i)(1-p)^n-1

but im looking to see if thats right?

Thanks

2. Oct 22, 2005

oh and by the way... that (nCk) or (nCi) means "N choose k" or "N choose i"

3. Oct 22, 2005

### HallsofIvy

$$\Sigma_{i= k}^n _nC_i p^i(1- p)^{n-i}$$

NOT "i= k to the n", that would be i= kn!

And it is (1-p)n-i, not (1-p)n-1.

4. Oct 22, 2005