Week 2
Probability: The study of randomness and uncertainty
Probability: Assumes properties of population are known and uses mathematics to answer questions about what we expect to see in a sample of observations drawn from that population
Statistics: Uses sample of observations to draw conclusions about the population from which the sample was take
Experiment: An action or process that generates observations. The sample space is the set of all possible outcomes of an experiment. An event is a collection of outcomes contained in the sample space. A simple event contains a single outcome.
Use set theory to study relationships among events.
_{AB: The set containing all outcomes that are in A OR in B OR in both.}
A
_{}B
: The set containing all outcomes that are in A AND in BA': The set containing all outcomes that are NOT in A
S: Denotes the set containing all possible outcomes of an event.
_{}: The empty set, containing no outcomes (the complement of S, S ' )
Probability measures must obey the following rules:
The probability of an event, A, can be interpreted as the proportion of times that event A would occur if the same experiment was carried out over and over again. (limiting relative frequency).
2. If A and B are mutually exclusive, | |
3. Additive law of probability: |