Confirming the Sum Notation: P(X ≥ k)

[rad0786]

The Sum Of...Σ

So we were given this awkward question to do out of the textbook... and a classmate and I arrived at similar 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 I am looking to see if that's right?

Thanks

 

[rad0786]

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

 

[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.

 

[rad0786]

oh... how do you make your equations look so nice? I believe that its some softwear that you use?