Week 1: Introduction to Probability
Experiment: activity that results in 1 of several possible outcomes.
Outcomes must be mutually exclusive & collectively exhaustive
Mutually exclusive: no 2 outcomes can occur together
Collectively exhaustive: at least 1 of the outcomes must occur when the experiment is performed
1st law of prob: the prob of any event is a number between 0 and 1.
Rule of complement: the complement of A, denoted by A bar, is the event that A does not occur.
2nd law of prob: if A and B are mutually exclusive, then
Relative frequency: proportion of times that the event occurs out of the number of times the
random experiment is run
Objective prob: those that can be estimated from long-run proportions
Subjective prob: those that cannot be estimated from long-run proportions, usually opinions
,Week 2: Basic Probability Theory
Conditional prob: the prob of an event given that another event has occurred
Requires the assumption of independence
Bayes’ theorem: begin with initial or prior prob for certain events. Obtain additional info. Calculate
revised or posterior prob.
Needs to be mutually exclusive & collectively exhaustive
Independent event: knowing whether 1 event has occurred will not change our assessment of the
other event.
Events cannot be mutually exclusive & independent at the same time.
Mutually exclusive events are dependent events
, Week 3: Discrete Probability
Video 2:
Random variable: assigns a numerical value to each possible outcome of a probabilistic experiment.
Random variable can be discrete or continuous.
Video 3:
Prob distribution: a random variable describes how probs are distributed over the values of a
random variable
A discrete prob distribution consists of possible values & corresponding probs that are mutually
exclusive exhaustive.
Histogram: display the probs as a bar chart.
Video 4 & 5:
Summary statistics: used to summarise a set of observations in order to communication the largest
amount as simply as possible.
Measure of location or central tendency: such as mean, median mode
Measure of statistical dispersion: SD, variance, range
Measure of the shape of distribution: skewness or kurtosis
Mean = SUMPRODUCT ( range of x , range of prob )
Variance = SUMPRODUCT ( square of x , range of prob ) – mean^2
SD = SQRT ( variance )
Experiment: activity that results in 1 of several possible outcomes.
Outcomes must be mutually exclusive & collectively exhaustive
Mutually exclusive: no 2 outcomes can occur together
Collectively exhaustive: at least 1 of the outcomes must occur when the experiment is performed
1st law of prob: the prob of any event is a number between 0 and 1.
Rule of complement: the complement of A, denoted by A bar, is the event that A does not occur.
2nd law of prob: if A and B are mutually exclusive, then
Relative frequency: proportion of times that the event occurs out of the number of times the
random experiment is run
Objective prob: those that can be estimated from long-run proportions
Subjective prob: those that cannot be estimated from long-run proportions, usually opinions
,Week 2: Basic Probability Theory
Conditional prob: the prob of an event given that another event has occurred
Requires the assumption of independence
Bayes’ theorem: begin with initial or prior prob for certain events. Obtain additional info. Calculate
revised or posterior prob.
Needs to be mutually exclusive & collectively exhaustive
Independent event: knowing whether 1 event has occurred will not change our assessment of the
other event.
Events cannot be mutually exclusive & independent at the same time.
Mutually exclusive events are dependent events
, Week 3: Discrete Probability
Video 2:
Random variable: assigns a numerical value to each possible outcome of a probabilistic experiment.
Random variable can be discrete or continuous.
Video 3:
Prob distribution: a random variable describes how probs are distributed over the values of a
random variable
A discrete prob distribution consists of possible values & corresponding probs that are mutually
exclusive exhaustive.
Histogram: display the probs as a bar chart.
Video 4 & 5:
Summary statistics: used to summarise a set of observations in order to communication the largest
amount as simply as possible.
Measure of location or central tendency: such as mean, median mode
Measure of statistical dispersion: SD, variance, range
Measure of the shape of distribution: skewness or kurtosis
Mean = SUMPRODUCT ( range of x , range of prob )
Variance = SUMPRODUCT ( square of x , range of prob ) – mean^2
SD = SQRT ( variance )
