Probability and probability distributions Flashcards
Define: Population
Also called the sample space.
All the possible outcomes of such an experiment.
for example {HH,HT,TH,TT}
Define: Random experiment
Where there is uncertainty about which outcome will actually realise.
Define: Event
is a certain collection of outcomes (or subset of the sample space), e.g., HH and HT.
Explain: Mutually exclusive
the occurrence of one event prevents the occurrence of another event at the same time.
Explain: Equally exclusive
if we are confident that one event is as likely to occur as the other event.
Explain: Collectively exhaustive
if they exhaust all possible outcomes of an experiment. In our coin-tossing example, since HH, HT, TH, and TT are the only possible outcomes, they are (collectively) exhaustive events.
Define: Variable
is the outcome of an experiment, described numerically.
When is a variable stochastic or random?
when its numerical value is determined by the outcome of an experiment.
Explain: Discreet random variable
takes on a finite number of values e.g., 0, 1, 2.
Explain: Continuous random variable
takes on values in some interval e.g., a height range of 60-72 inches.
Define: Absolute frequency
number of occurrences of a given event
Define: Relative frequency
absolute number divided by total number of occurrences = probability
Characteristics of probabilities
Probability lies between 0 and 1.
If event A, B, C are mutually exclusive, the probability that any one of them will occur = sum of their individual probabilities
The sum of all the probabilities in a sample space must equal 1.
when are events statistically independent?
if the probability of them occurring together = product of their individual (or marginal) probabilities
How to determine the marginal probability of X
Add the joint probabilities that coincide with given X-values, regardless of the values taken by Y.
Thus, sum down the column.
