Flashcards
S2
Flashcards do conjunto (20)
- 1Assumptions 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) - 2X~B(n,p)\(P(X=x)=\binom{n}{r}p^r(1-p)^{n-r}\)
\(E(X)=np\)
\(Var(X)=npq\) where \(q=1-p\) - 3You can switch from success X to failure YX~B(20,0.7)
Y~B(20,0.3) - 4When switching from probability of successes X to failures Y, flip the inequality (but preserve < vs \(\leq\))\(P(Xn-k)\)
\(P(X\leq k)=P(Y\geq n-k)\) - 5\[P(X>1) = 1-P(X\leq 1)\] \[P(X\geq 1) = 1-P(X=0)\]Don't forget to define your random variable
"Let X be the number of heads in 10 spins"
X~B(10,0.75) - 6Poisson: approximation to the normalWhen mean is large \((\lambda>10)\)
X~Po\((\lambda) \implies X\approx N(\lambda,\lambda)\) - 7Binomial: approximation to the normalWhen \(np>10\) and \(nq>10\), then X~B(n,p) \(\implies X\approx N(\mu,\sigma^2)\) where
\(\mu = np\) and \(\sigma^2 = npq\) - 8Remember when approximating to the normal ...Continuity correction
- 9Continuity corrections: extend your range by 0.5 at each end\(P(X\leq5)=P(Y\leq5.5)\)
\(P(X\geq6)=P(Y\geq5.5)\)
\(P(4\leq X\leq5)=P(3.5\leq Y\leq5.5)\) - 10Binomial: approximation to PoissonWhen \(n>50\) and \(p<0.1\), then X~B(n,p) \(\implies\) X~Po(np)
c.c. not necessary as still discrete - 11Conditions required for Poisson- Events occur independently
- Events occur singly in time
-A fixed rate for which events occur - 12Positive skewmean>median>mode
- 13Negative skewmean
- 14statistica random variable that is a function of the sample which contains no unknown quantities/parameters
- 15populationthe collection of all items
- 16samplesome subset of the population which is intended to be representative of the population
- 17censuswhen the entire population is sampled
- 18sampling unitindividual member or element of the population or sampling frame
- 19sampling frameA list of all sampling units or all the population
- 20Sampling distributionAll possible samples are chosen from a population (1); the values of a statistic and the associated probabilities is a sampling distribution (1).