20 terms

random variable

takes numerical values that describe the outcome of some chance process

probability distribution

gives the random variable's possible values and their probabilities (v & p)

discrete random variable

takes a fixed set of possible values with gaps between

mean (expected value) of a discrete random variable

1. multiply each possible value by its probability

2. add all the products

*not a possible value of the random variable, a "long-run average"

2. add all the products

*not a possible value of the random variable, a "long-run average"

variance

standard deviation squared; must find variance first and then square root it to find standard deviation (can never add standard deviations)

continuous random variable

takes all values in an interval of numbers; probability distribution of X is described by a density curve

standard deviation of a random variable

cannot add or subtract, only multiply/divide

independent random variables

when knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone

sum of random variables

mean = mean(x) + mean(y)

binomial setting

arises when several independent trials of the same chance process are performed and the number of times that a particular outcome occurs is recorded;

BINS

Binary? the possible outcomes of each trial can be classified as "success" or "failure"

Independent? trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial

Number? the number of trials n of the chance process must be fixed in advance

Success? on each trail, the probability p of success must be the same

Independent? trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial

Number? the number of trials n of the chance process must be fixed in advance

Success? on each trail, the probability p of success must be the same

binomial random variable

the count X of successes in a binomial setting

binomial distribution

probability distribution of X with parameters n and p

Possible values --> 0 < x < n

mean = np

standard deviation = (square root) np(1-p)

Possible values --> 0 < x < n

mean = np

standard deviation = (square root) np(1-p)

binomial coefficient

the number of ways of arranging k successes among n observations

binomial probability

the number of different ways in which k successes can be arranged among n trials, multiplied by the probability of any one specific arrangement of the k successes

sampling without replacement condition

when taking an SRS of size n from a population of size N, we can use a binomial distribution to model the count of successes in the sample as long as n is less or equal to 10% of N

geometric setting

arises when independent trials of the same chance process are performed and the number of trials until a particular outcome occurs is recorded

BITS

Binary? the possible outcomes of each trial can be classified as "success" or "failure"

Independent? trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial

Trials? the goal is to count the number of trials until the first success occurs

Success? on each trail, the probability p of success must be the same

Independent? trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial

Trials? the goal is to count the number of trials until the first success occurs

Success? on each trail, the probability p of success must be the same

geometric random variable

the number of trials Y that it takes to get a success in a geometric setting

mean = 1/p

standard deviation = (square root) (1-p)/(p^2)

mean = 1/p

standard deviation = (square root) (1-p)/(p^2)

geometric probability

P(Y=k) = (p)(1-p)^(k-1)