AP Stats Unit 6 Vocabulary

Random Variable

Takes numerical values that describe the outcomes of some chance process.

Discrete random variables

A random variable that may assume either a finite number of values or an infinite sequence of values.

Probability distribution

Gives a random variable's possible values and their probabilities.

Expected Value

The expected value of a random variable is its theoretical long-run average value, the center of its model. Denoted u or E(X), it is found by summing the products of variable values and probabilities.

Mean (expected value) of a random variable

Multiply each possible value by its probability, then add all the products.

Variance of a random variable

An "average" of the squared deviation {(xi minus the mean of x) squared} of the values of the variable X from its mean.

Standard deviation

The square root of the variance.

Continuous random variable

Takes all values in an interval of numbers. The probability distribution of X is described by a density curve. The probability of any event is the area under the density curve and above the values of X that make up the event.

Linear Transformation

Adding or subtracting a constant (a), multiplying or dividing by a constant (b), or both. We write a linear transformation of the random variable X in the form Y = a + bx.

Linear Transformations (Adding/Subtracting and Multiplying/Dividing)

Adding/Subtracting:
Adds (a) or subtracts (a) from measures of center and location (mean, median, quartiles, percentiles). Does not change the shape or measures of spread (range, IQR, standard deviation).

Multiplying/Dividing:
Multiplies or divides measures of center and location (mean, median, quartiles, percentiles) by (b). Multiplies or divides measures of spread (range, IQR, standard deviation) by (b). Does not change the shape of the distribution.

Independent random variables

Knowing the value of one variable does not tell you anything about the value of the other.

Binomial setting

consists of (n) independent trials of the same chance process, each resulting in a success or a failure, with probability of success (p) on each trial.

Four conditions of a binomial setting (BINS)

B: Binary; The possible outcomes of each trial can be classified as "success" or "failure."
I: Independent; Trials must be independent, that is knowing the result of one trial must not tell us anything about the result of any other trial.
N: Number; The number of trials (n) of the chance process must be fixed in advance.
S: Success; There is the same probability of success on each trial.

Binomial random variable

The count of X successes in a binomial setting.

Binomial distribution

The probability distribution of X in a binomial setting.

Binomial coefficient

The number of ways of arranging (k) successes among (n) observations.

Large Counts condition

When np is greater than or equal to 10 and n(1-p) is greater than or equal to 10.

Geometric setting

Consists of repeated trials of the same chance process in which the probability (p) of success is the same on each trial, and the goal is to count the number of trials it takes to get one success.

Geometric random variable

If Y = the number of trials required to obtain the first success, then Y is a geometric random variable.

Geometric distribution

The probability distribution of Y in a geometric setting.

Normal approximation

Says that if X is a count of successes having the binomial distribution with parameters n and p, then when n is large, X is approximately normally distributed with mean np and standard deviation square root of np(1-p).