chapter 5: discrete random variables Flashcards
what is a random variable
a variable whose value is numerical and is determined but the outcome of an experiment
it assigns only one numerical value to each experiment outcome
a discrete random variable
a random variable who’s possible values can be counted or listed
if you can count them, it can be an infinite number of values
continuous random variable
when a random variable can assume any numerical value in one or more intervals on the real number line
how can we model a random variable?
by finding its probability distribution
probability distribution, what does it do?
it describes how probabilities are distributed over values
of the random variable
what is a discrete probability distribution?
probability of a discrete random variable
table, graph, or formula
gives probability associated with each possible value that the random variable can assume
what is p(x)
probability distribution of x
x: discrete random variable
what are the two conditions of a discrete probability distribution?
- p(x) = or > 0
2. the sums of p(x) must be all = to 1
how is the population mean called when dealing discrete random variables
the expected value (or mean) of a discrete random variable
how to calculate the expected value (or mean) of a discrete random variable?
multiply each value of x by p(x)
sum resulting products over all values of x
which is the most important discrete probability distribution
the binomial distribution
what are the characteristics of the binomial distribution (binomial model)
- experiment consists of n identical trials
- each trial results in success or failure
- probability of success = p
probability of failure = q = 1 - p
- the trials are independent
what is x in the binomial model
the total amount of successes in n trials
it is the binomial random variable
what is the rare event approach to a statistical interference?
if the probability of an observed sample is small, then we have strong evidence that the assumption is false
whines the probability of an observed sample considered to be small?
when it is less than 0.5
