AP Statistics Chapter 6 Random Variables

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Terms in this set (...)

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"
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
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)
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
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)
geometric probability
P(Y=k) = (p)(1-p)^(k-1)