S2

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Stats Edexcel
Joanne Moss
Fichas por Joanne Moss, actualizado hace más de 1 año
Joanne Moss
Creado por Joanne Moss hace más de 7 años
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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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