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Stats · #3 July 6th, 2009, 02:33 AM

Quote:

Originally Posted by mr fantastic

where X ~ Binomial(n, p).

And it's trial, not trail.

Please let me know where if i am right or no?

Answer:
Binomial P(x;n, $\theta$ ) = $\binom{n}{x} \theta ^x (1- \theta)^{n-x})$

Probability of atleast 1 success is

$1-P(X=0)$ = $1 -\binom{n}{0} \theta ^0 (1- \theta)^{n-0}$ = $1 - (1 - \theta)^n$

Probability of k success occuring in first n trials is
$P(X=k) = \binom{n}{k} \theta^k (1- \theta)^{n-k}$

Probability of all trials being success is
$P(X=n) = \binom{n}{n} \theta^n (1- \theta)^{n-n} = 0$