Assumptions of a Binomial Distribution

X~B(n,p)

You can switch from success X to failure Y

When switching from probability of successes X to failures Y, flip the inequality (but preserve < vs \(\leq\))

\[P(X>1) = 1-P(X\leq 1)\]
\[P(X\geq 1) = 1-P(X=0)\]

Poisson: approximation to the normal

Binomial: approximation to the normal

Remember when approximating to the normal ...

Continuity corrections: extend your range by 0.5 at each end

Binomial: approximation to Poisson

Conditions required for Poisson

Positive skew

Negative skew

statistic

population

sample

census

sampling unit

sampling frame

Sampling distribution