AP Statistics Vocabulary - Chapter 6

Binomial Probability

If X has the binomial distribution with n trials and probability p of success on each trial, the possible values of X are 0, 1, 2...n. If k is any one of these values, P(X=k)=(n given k)p^k(1-p)^n-k.

Normal Approximation for Binomial Distributions

If X is a count having the binomial distribution with parameters n and p, then when n is large, X is approximately Normally distributed with mean no and standard deviation square root of np(1-p). We will use this approximation when no is greater than or equal to 10 and n(1-p) is greater than or equal to 10.

Geometric Probability

If Y has the geometric distribution with probability p of success on each trial, the possible values of Y are 1, 2, 3, ... If k is any one of these values, P(Y=k)=(1-p)^k-1 x p.

Mean (Expected Value) of a Geometric Random Variable

If Y is a geometric random variable with probability of successes p on each trial, then it's mean is 1/p. That is, the expected number of trials required to get the first success is 1/p.

Mean and Standard Deviation of a Binomial Random Variable

If a count X has the binomial distribution with number of trials n and probability of successes p, the. It's mean and standard deviation np and square root of np(1-p).

Independent Random Variables

If knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone, and vice versa, the. X and Y are independent random variables. That is, there is no association between the values of one variable and the values of the other.

Binomial Distribution

In a binomial setting, suppose we let X equal the number of successes. The probability distribution of X has a binomial distribution with parameter n and p, where n is the number of trials of the chance process and p is the probability of a success on any one trial. The possible values of X are whole numbers from zero to n.

Geometric Distribution

In a geometric setting, suppose we let Y= the number of trials required to get the first success. The portability distribution of Y is a geometric distribution with parameters p, the probability of a success on any trial. The possible values of Y are 1, 2, 3, ...

Mean (Expected Value) of a Discrete Random Variable X

To find the mean of X, multiply each possible value by its probability, then add all the products.

Geometric Setting

A geometric setting arises when we perform independent trials of the same chance process and record the number of trials until a particular outcome occurs. The four conditions are: Binary (success or failure), Independent (each outcome doesn't affect the next), Trials (do experiments until 1st success), Success (each success probability is the same).

Linear Transformation

A linear transformation of a random variable involves adding a constant a, multiplying by a constant b, or both. We can write a linear transformation of the random variable X in the form Y= a + bX.

Binomial Setting

Arises when we perform several independent trials of the same chance process and record the number of times that particular outcome occurs. The four conditions are: Binary (success and failure), Independent (each outcome has no effect on the next), Number (set number of trials), and Success (the portability of success is the same for each sample).

Factorial

For any positive whole number n, its factorial n! Is n!=n x (n-1) x (n-2) x ... x 3 x 2 x 1. In addition, we define 0! = 1.

Variance of the Sum (Difference) of Independent Random Variables

For any two independent random variables X and Y, is T=X+Y, then the variance of T is sigma squared of T=sigma squared X + sigma squared Y. If D = X - Y, then the variance of D is the same as with T.

Mean of the Sum (Difference) of Random Variables

For any two random variables X and Y, if T=X+Y then the mean if T is equal to the mean of y plus the mean of X. If D=X-Y, the. The mean of D is the difference between X's and Y's means. In general, the mean of the sum of several random variables is the sum of their means.

Discrete Random Variable

Takes a fixed set of possible values with gaps between. The probability distribution of a discrete random variable gives its possible values and their probabilities. The probability of any event is the sum of the probabilities for the values of the variable that make up the event.

Continuous Random Variable

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

Random Variable

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

Variance of a Random Variable

The average squared deviation of the values of the variable from their mean.

Binomial Random Variable

The count X of successes in a binomial setting.

Mean (Expected Value) of a Random Variable

The mean is a random variable is the balance point of the probability distribution histogram or density curve. Since the mean is the long-run average value of the variable after many twos of the chance process, it is also known as the expected value of the random variable.

Geometric Random Variable

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

Binomial Coeffiecent

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

Probability Distribution

The probability distribution of a random variable gives its possible values and their probabilities.

Standard Deviation of a Random Variable

The square root of the variance of a random variable. The standard deviation measures the variability of the distribution about the mean.