8987622
Description
Flashcards by Joanne Moss, updated more than 1 year ago
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Created by Joanne Moss
over 7 years ago
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| Question | Answer |
| 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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