Stats: Chapter 10

Has unpredictable behavior in the short run but has a regular and predictable pattern in the long run

• Studies the likelihood of occurrence of random events in order to predict the behavior of defined systems.
• Only describes what happens in the long run

• The set of all possible outcomes in a random phenomenon
• The set of all outcomes are caleld events
• 1 event is the subset of the sample space

Description of a random phenomenon consisting of a sample space S and a way of assigning probabilities to events

• A number between 0 - 1 is a probability number
• All possible outcomes together must have a probability of one
• If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities
• The probability that an event occurs is 1 minus the probability that the event does not occur

e.g. If event 1 occurs 50% of the time and a diff event occurs 25% of the time, then the chance of one or the other occuring is 75%

• 0 = never occurs
• 1 = always occurs
• 0.5 occurs half the trials

A number between 0 - 1 is a probability number

The sample space S always equals 1

• If A and B are disjoints if they have no outcomes in common
• The chance of one of them occuring is the sum of the two probabilities

The probability of an event that does not occur is 1 - the probability that the event does occur

• A model with a finite sample (has limits)
• The prob of any event is the sum of the probabilities of all the values that make up the event
• This model assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1

• Assigns the probabilities as areas under a density curve
• The probability of any event is the area under the curve above the values that make up the event

A variable whose value is a numerical outcome of a random phenomenon

The random variable X tells us what the possible values of X are and how probabilities are assigned to those values