Chapter 2 : Review of Probability

outcome

one possible result of a random process

sample space

the set of all possible outcome

event

a subset of the sample space

random variable

a variable that assigns a numeral value to each possible outcome

discrete rv

countable number

continuous rv

range

cumulative distribution function

Probability that M is less than a particular value

expected value

the probability-wieghted a erage of a rv over repeated trials

variance

measures the duspersion of values around the expected value

standard deviation

square root of variance, same units as the original variable

skewness

measure asymmetry

kurtosis

describe the heaviness of the distribution’s tails

moment

expected value of a power of a rv

joint distribution

multiple rvs take on a value

marginal distribution

distribution of one variable, ignoring the other

conditional distribution

distribution of one variable, given the value of the other

covariance

whether two variables tend to move together

random sample

observations drawn from the same population inependently

i.i.d

independent and identically distributed

sample mean

average of the observations in a sample

sampling distribution

probability distribution of a statistics across repeated samples

finite-sample distribution

the exact distribution of a statistic for a given sample size

asymptotic distribution

a limiting distribution used to approximate a statistic as the sample size grows

consistency

a proprety of an estimator that means it converges in probability to the true parameter