# Stats 5ls

version from 2016-11-20 22:16

## Section

discreteprobability model made up of a list of individual outcomes
density curve curve that is always on or above the horizontal axis, has an area of 1 underneath
discrete vs continuous random variablesdiscrete must be a whole number, continuous can be any value, decimals included.
riskp of undesirable outcome
oddsp of undesirable outcome/ 1-p
disjoint events a and b are disjoint if they have no outcomes in common
p (b given a) = P(a and b) / P(a)
independentknowing that one event occurs dont not change the probability we would assign to the other events
P(at least one event occurs)p(a) + p(b) + p(c) +.........
P(all events occur)P(a) x P(b) x.........
p(a or b)p(a) + p(b) - p(a and b)
p(a and b)p(a) x p(b given a)
bayes theorem P(a given b) = p(b given a)p(a)/ p(b given a1)p(a1) + p(b given a2)p(a2)+ ........
binomial conditionsfixed n observations, all observations independent, each observation falls is either a success or failure, probability of success is the same for each observation
binomial mean np
binomial probabiltyp(x=k) = p^k (1-p)^n-k
n choose r = n!/ r!(n-r)!
when to estimate with normal distributionnp greater than or = 10, n(1-p) greater than or = 10
normal curve rule(1 sd) contains 68-2 sd contain 95-3 sd contain 99.7
z scorex- mean/ standard dev. tells the number of standard deviations away from the mean something is
cumulative proportionarea of normal curve at and below a given point
z proportiontells you amount less than or equal to
permutatonsnPk= n!/(n-k)!
combinationsnCk= n!/[(k!)(n-k)!]
parameternumber that describes a population, (ex- mu)
statisticnumber that can be computed from the sample data without making use of any unknown parameters. (ex- x bar)
standard deviation of a sample meansd/radical n
standard deviation of a sample proportionradical [p(1-p)/n]
when n, np, and n(1-p) are large, and the population is at least 20 x larger than the sample, sd=radical [np(1-p)/n]
central limit theoremfor any distribution, as n increases the distribution becomes more normal if it has a stable standard deviation