wk9 - Random variables and probability distributions

Random variable

assigns a value to each event in a sample space. The events are mutually exclusive and collectively exhaustive

distribution

defines the set of values that a random variable can take and how likely each value is

Discrete random variable

a finite or at most countable infinite number of distinct values

Continuous random variable

assumes an uncountably infinite number of values

Probability mass function

function that defines the probability that each value occurs

Discrete numbers

natural, 0,1,2,3… - integers, -1,1 etc., there are gaps

Continuous numbers

real numbers. There are NO gaps

Central limit theorem

the distribution of the sample mean will approximate normal as the number of samples of size n goes to infinity, regardless of the underlying frequency distribution (this only applies to random samples)

Sampling distribution

the probability distribution of a sample statistic if the number of samples goes to infinity

normal distribution

a bell shaped statistical distribution that can be entirely characterized by its mean and sd

standard error of the mean

the sd of the sampling distribution of sample means

frequency distribution

distribution of actual scores in a sample

confidence interval

a probabilistic statement about the likely value of a population characteristic based on the observations in a sample

independent outcomes

two or more outcomes such that the realization of one of the outcomes does not affect the realization of the other outcomes