S2 | Karteikarten

Frage	Antworten
Assumptions of a Binomial Distribution	- Fixed number of trials - Each trial has 2 outcomes (success/failure) - Constant probability of success - Each trial is independent (make sure this is in context)
X~B(n,p)	$P(X=x)=\binom{n}{r}p^r(1-p)^{n-r}$ $E(X)=np$ $Var(X)=npq$ where $q=1-p$
You can switch from success X to failure Y	X~B(20,0.7) Y~B(20,0.3)
When switching from probability of successes X to failures Y, flip the inequality (but preserve < vs $\leq$ )	$P(X<k)=P(Y>n-k)$ $P(X\leq k)=P(Y\geq n-k)$
$P(X>1) = 1-P(X\leq 1)$ $P(X\geq 1) = 1-P(X=0)$	Don't forget to define your random variable "Let X be the number of heads in 10 spins" X~B(10,0.75)
Poisson: approximation to the normal	When mean is large $(\lambda>10)$ X~Po $(\lambda) \implies X\approx N(\lambda,\lambda)$
Binomial: approximation to the normal	When $np>10$ and $nq>10$ , then X~B(n,p) $\implies X\approx N(\mu,\sigma^2)$ where $\mu = np$ and $\sigma^2 = npq$
Remember when approximating to the normal ...	Continuity correction
Continuity corrections: extend your range by 0.5 at each end	$P(X\leq5)=P(Y\leq5.5)$ $P(X\geq6)=P(Y\geq5.5)$ $P(4\leq X\leq5)=P(3.5\leq Y\leq5.5)$
Binomial: approximation to Poisson	When $n>50$ and $p<0.1$ , then X~B(n,p) $\implies$ X~Po(np) c.c. not necessary as still discrete
Conditions required for Poisson	- Events occur independently - Events occur singly in time -A fixed rate for which events occur
Positive skew	mean>median>mode
Negative skew	mean<median<mode
statistic	a random variable that is a function of the sample which contains no unknown quantities/parameters
population	the collection of all items
sample	some subset of the population which is intended to be representative of the population
census	when the entire population is sampled
sampling unit	individual member or element of the population or sampling frame
sampling frame	A list of all sampling units or all the population
Sampling distribution	All possible samples are chosen from a population (1); the values of a statistic and the associated probabilities is a sampling distribution (1).

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