Preface
Here are the course lecture notes for the course MAS108, Probability I, at Queen
Mary, University of London, taken by most Mathematics students and some others
in the first semester.
The description of the course is as follows:
This course introduces the basic notions of probability theory and de-
velops them to the stage where one can begin to use probabilistic
ideas in statistical inference and modelling, and the study of stochastic
processes. Probability axioms. Conditional probability and indepen-
dence. Discrete random variables and their distributions. Continuous
distributions. Joint distributions. Independence. Expectations. Mean,
variance, covariance, correlation. Limiting distributions.
The syllabus is as follows:
1. Basic notions of probability.
Sample spaces, events, relative frequency,
probability axioms.
2. Finite sample spaces. Methods of enumeration. Combinatorial probability.
3. Conditional probability. Theorem of total probability. Bayes theorem.
4. Independence of two events. Mutual independence of
n
events. Sampling
with and without replacement.
5. Random variables. Univariate distributions - discrete, continuous, mixed.
Standard distributions - hypergeometric, binomial, geometric, Poisson, uni-
form, normal, exponential. Probability mass function, density function, dis-
tribution function. Probabilities of events in terms of random variables.
6. Transformations of a single random variable.
Mean, variance, median,
quantiles.
7. Joint distribution of two random variables. Marginal and conditional distri-
butions. Independence.
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