Set Algebra

Question 1

How would you define an event in terms of set algebra?

Answer 1

An event is a set of sample points, w, or elementary events.

Question 2

Disjoint events

Answer 2

Also known as a “mutually exclusive”, is when two events A and B cannot happen at the same time.

Therefore, A intersection B = empty

Question 3

Experiment

Answer 3

Defined as the performance of some actions

Question 4

Random Experiment

Answer 4

Is one for which the outcome is uncertain. There is nothing random about it once we performed the experiment and observed the outcomes.

Question 5

Sample space

Answer 5

The set of all possible outcomes of a random experiment.

Denoted by the letter S.

Question 6

Elementary outcome

Answer 6

Element w that belongs to S.

Question 7

Tip 1:

Remember that how you define S, it might help you to use some tools rather than others.

Answer 7

Example:

6 Green and 4 Red marbles:

S = {R,G}

OR

S={1,2,3,4,5,6,7,8,9,10}

where numbers 1-4 are red and 5-10 are green.

Question 8

Set Functions

Answer 8

A real-valued function P( . ) is a function that gives a real number, P(A), for every event A.