30 Mar 2012

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Chapter 18

Probability Models

Probability Models

“at random” we give every such subject the same chance to be the one we choose

P(not married) = P(never married) + P(widowed) + P(divorced)

P(not married) = the probability that the woman we choose is not married

A probability model for a random phenomenon describes all the possible outcomes and says

how to assign probabilities to any collection of outcomes (events)

Probability Rules

A) Any probability is a number between 0 and 1

B) All possible outcomes together must have probability 1

C) The probability that an event does not occur is 1 minus the probability that the event does

occur

D) If two events have no outcomes in common, the probability that one or the other occurs is the

sum of their individual probabilities

Any assignment of probabilities to all individual outcomes that satisfies Rules A and B is

legitimate (Rules C and D are then automatically true)

The rules tells us only what probability models make sense

They don’t tell us whether the probabilities are correct, whether they describe what actually

happens in the long run

Personal probabilities that don’t obey Rules A and B are incoherent (don’t go together in a way

that makes sense)

Probability models for sampling

Choosing a random sample from a population and calculating a statistic such as the sample

proportion is certainly a random phenomenon

The distribution of the statistic tells us what values it can take and how often it takes those values

A statistic from a large sample has a great many possible values

The sampling distribution of a statistic tells us what values the statistic takes in repeated

samples from the same population and how often it takes those values

Because there are usually many possible values, sampling distributions are often described by a

density curve such as a Normal Cuve