STA220H5 Chapter Notes - Chapter 2.8: Sample Space
2.8 and 3.1
An experiment is an act or process of observation that leads to a single outcome that
cannot be predicted with certainty.
A sample point is the most basic outcome of an experiment.
The sample space of an experiment is the collection of all its sample points.
Probability rules for sample points
Let pi represent the probability of sample point i. then
1. All sample point probabilities must lie between 0 and 1 (i.e., 0<pi<1).
2. The probabilities of all the sample points within a sample space must sum to
1 (i.e., pi=1).
An event is a specific collection of sample points.
Probability of an event
The probability of an event A is calculated by summing the probabilities of the
sample points in the sample space for A.
Steps for calculating probabilities of events
1. Define the experiment; that is, describe the process used to make an
observation and the type of observation that will be recorded.
2. List the sample points.
3. Assign probabilities to the sample points.
4. Determine the collection of sample points contained in the event of interest.
5. Sum the sample point probabilities to get the probability of the event.
Combinations rule
Suppose a sample of n elements is to be drawn without replacement from a set of N
elements. Then the number of different samples possible is denoted by (N n) and is
equal to
Where
n! = n (n-1) (n-2) . . . (3) (2) (1)
and similarly for N! and (N-n)! for example, 5! = 5 . 4 . 3 . 2 . 1. [note: the quantity 0!
Is defined to be equal to 1.]
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty. A sample point is the most basic outcome of an experiment. The sample space of an experiment is the collection of all its sample points. Let pi represent the probability of sample point i. then: all sample point probabilities must lie between 0 and 1 (i. e. , 0
