CS1 – Actuarial Statistics 1 Tutorials

CS1 Aim

The aim of the Actuarial Statistics 1 subject is to provide a grounding in mathematical and statistical techniques that are of particular relevance to actuarial work.

Competences

On successful completion of this subject, a student will be able to:

1.   describe the essential features of statistical distributions.
2.   summarise data using appropriate statistical analysis, descriptive statistics and graphical presentation.
3.   describe and apply the principles of statistical inference.
4.   describe, apply and interpret the results of the linear regression model and generalised linear models.
5.   explain the fundamental concepts of Bayesian statistics and use them to compute Bayesian estimators.

Links to other subjects

CS2 builds directly on the material in this subject.

CM1 and CM2 apply the material in this subject to actuarial and financial modelling.

This subject assumes that a student will be competent in the following elements of foundational mathematics and basic statistics:

1.   Summarise the main features of a data set (exploratory data analysis)
   1.1  Summarise a set of data using a table or frequency distribution, and display it graphically using a line plot, a box plot, a bar chart, histogram, stem and leaf plot or another appropriate elementary device.1.2  Describe the level/location of a set of data using the mean, median, mode, as appropriate.1.3  Describe the spread/variability of a set of data using the standard deviation, range, interquartile range, as appropriate.1.4  Explain what is meant by symmetry and skewness for the distribution of a set of data.
2. 2  Probability
   2.1  Set functions and sample spaces for an experiment and an event.2.2  Probability as a set function on a collection of events and its basic properties.2.3  Calculate probabilities of events in simple situations.2.4  Derive and use the addition rule for the probability of the union of two events.

   2.5  Define and calculate the conditional probability of one event given the occurrence of another event.

   2.6  Derive and use Bayes’ theorem for events.

   2.7  Define independence for two events, and calculate probabilities in situations involving independence.

3.  Random variables
   3.1  Explain what is meant by a discrete random variable, define the distribution function and the probability function of such a variable, and use these functions to calculate probabilities.3.2  Explain what is meant by a continuous random variable, define the distribution function and the probability density function of such a variable, and use these functions to calculate probabilities.3.3  Define the expected value of a function of a random variable, the mean, the variance, the standard deviation, the coefficient of skewness and the moments of a random variable, and calculate such quantities.3.4  Evaluate probabilities associated with distributions (by calculation or by referring to tables as appropriate).

   3.5  Derive the distribution of a function of a random variable from the distribution of the random variable.