AP Statistics / Unit 2: Probability, Random Variables, and Probability Distributions
2.10 The Binomial Distribution
Notes
Binomial setting: fixed $n$ trials, two outcomes, constant $p$, independent trials.
$$P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$$
- $\mu=np$, $\displaystyle \sigma=\sqrt{np(1-p)}$.
Practice
$n=10$, $p=0.3$. $\mu_X=$
$np$.
Using the same $n$ and $p$, $\sigma_X\approx$
$\displaystyle \sqrt{10(0.3)(0.7)}=\sqrt{2.1}$.
Which is NOT a binomial condition?
BINS: binary, independent, number fixed, same $p$.
Ready for more? Take the Unit 2 test.