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ap stats chapter 6
chapter 6 OP STAT TERMS
| Term | Definition |
|---|---|
| probability | the chances of something to occur in all possible subjective options and ways it can, doesnt neccesarily gaurantee much. |
| random process | generates outcomes that are determined purely by chance. |
| probability | generates outcomes that are determined purely by chance. |
| law of large numbers | says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability. |
| simulation | imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes. |
| event | is any collection of outcomes from some random process. |
| complement rule | says that 𝑃(A𝐶)=1−𝑃(A, where A𝐶 is the complement of event A; that is, the event that A does not occur. |
| Venn diagram | consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the random process. |
| Conditional probability | The probability that one event happens given that another event is known to have happened is called a conditional probability. The conditional probability that event A happens given that event B has happened is denoted by 𝑃(A|B). |
| independent events | if knowing whether or not one event has occurred does not change the probability that the other event will happen. |
| General multiplication rule | For any random process, the probability that events A and B both occur can be found using the general multiplication rule: P ( A and B) = P ( A n B) = P(a)x p(b/a) |
| tree diagram | shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities. |
| random variable | takes numerical values that describe the outcomes of a random process. |
| probability distribution | of a random variable gives its possible values and their probabilities. |
| discrete random variable | X takes a fixed set of possible values with gaps between them. |
| mean (expected value) of a discrete random variable | is its average value over many, many trials of the same random process. |
| standard deviation of a discrete random variable | measures how much the values of the variable typically vary from the mean in many, many trials of the random process. |
| continuous random variable | can take any value in an interval on the number line. |
| Independent random variables | two random variables are independent if knowing the value of one variable does not change the probability distribution of the other variable. |
| Binomial random variable, | The count of successes X in a binomial setting is a binomial random variable. The possible values of X are 0, 1, 2, …, n. |
| Binomial distribution | The probability distribution of X is a binomial distribution. Any binomial distribution is completely specified by two numbers: the number of trials n of the random process and the probability p of success on each trial. |
| Binomial coefficient | The number of ways to arrange x successes among n trials |
| 10% condition | When taking a random sample of size n from a population of size N, we can treat individual observations as independent when performing calculations as long as n<.10 N |
| Large Counts condition | says that the probability distribution of X is approximately Normal if 𝑛 𝑝 ≥ 10 and 𝑛 ( 1−𝑝 ) ≥10 That is, the expected numbers (counts) of successes and failures are both at least 10. |
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