CS1 Actuarial Statistics
Probability, regression, and GLMs: the statistical toolkit every modern actuary uses daily.
About CS1
CS1 covers the statistical theory underlying all actuarial modelling: probability distributions, maximum likelihood estimation, regression, GLMs, Bayesian methods, and time series. As actuarial work becomes data-driven, CS1 has grown in strategic importance. Students who clear CS1 are immediately valuable to employers building pricing models and analytics tools.
Who is this for?
Students with A-level Maths or equivalent. Often taken alongside CM1. Students interested in data science, InsurTech, or analytics roles should prioritise CS1 early.
152 days until CS1, April 2027
CS1A 13 Apr · CS1B 15 Apr · entry closes in 85 days
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Learn CS1 free — 16 worked explainers
One idea per page, explained from scratch, each ending in a worked example with the arithmetic shown in full. These are the ideas students most often get stuck on in CS1. Start anywhere.
- Moment generating functions, and how to get moments out of them Write down a moment generating function, differentiate it to get the first three moments, and check them against the cumulant route
- The central limit theorem, and when the normal approximation is safe Apply the central limit theorem to a total and to a sample mean, add a continuity correction, and judge whether the approximation is safe
- Maximum likelihood estimation, step by step Derive a maximum likelihood estimator, confirm it is a maximum, and attach a standard error and a confidence interval to it
- Confidence intervals: what the 95% actually means Build a confidence interval for a mean and for a proportion, choose between t and z, and say correctly what the interval means
- Hypothesis testing and p-values, without the folklore Set up a one-sided test, compute and interpret a p-value, and work out the power of the test against a stated alternative
- Simple linear regression: least squares, fitted by hand Fit a least squares line by hand, test whether the slope is real, and explain what R-squared does and does not tell you
- Generalised linear models: the three parts, and the link function Say what the three components of a GLM are, read a log-link Poisson model as a set of multipliers, and test a factor using the deviance
- Bayesian estimation, conjugate priors and the credibility formula inside them Update a gamma prior with Poisson claim data, read off the posterior mean, and show it is a credibility weighted average of prior and data
- Conditional expectation, and the variance decomposition that comes with it Find a mean in two stages with the tower property, split a variance into its within and between parts, and check both against a direct calculation
- Sampling distributions: what the sample mean and sample variance actually do State the sampling distribution of the mean and of the sample variance for a normal sample, explain the n minus 1 divisor, and build an interval for a variance
- The method of moments, and when maximum likelihood is worth the extra work Fit a distribution by equating moments, state when the estimator is efficient and when it is not, and recognise the cases where it fails outright
- The likelihood ratio test, and why the Wald and score tests exist too Construct a likelihood ratio test, get its degrees of freedom right, and explain how the Wald and score statistics differ from it and from each other
- The chi-square goodness of fit test, and how to get its degrees of freedom right Compute a goodness of fit statistic, pool cells with small expected counts, get the degrees of freedom right and interpret the result honestly
- Contingency tables: testing whether two classifications are related Build expected counts under independence, test a contingency table, read its residuals, and show that a two-by-two table is the two-proportion test squared
- Analysis of variance: comparing three or more means at once Split a total sum of squares into between and within parts, build and interpret the F test, and compare group means afterwards without inflating the error rate
- Multiple linear regression, and what controlling for another variable really does Fit and interpret a two-predictor regression, explain a coefficient as a partial effect, build its ANOVA table and judge the damage collinearity does
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Complete Syllabus
- Probability: univariate and multivariate distributions, moments, generating functions
- Statistical inference: maximum likelihood, method of moments, Cramér-Rao lower bound
- Hypothesis testing: likelihood ratio test, Wald test, Neyman-Pearson lemma
- Confidence intervals: exact and approximate intervals, bootstrap methods
- Linear regression: OLS, model checking, F-tests, variable selection, multicollinearity
- Generalised Linear Models: Poisson, Gamma, inverse Gaussian, logistic regression
- Bayesian statistics: prior distributions, posterior, credibility theory, Bühlmann model
- Time series: stationarity, autocorrelation, ARIMA models, Box-Jenkins methodology
- Simulation: inverse transform method, acceptance-rejection, Monte Carlo applications
Career Outcomes
Actuarial Analyst, Pricing Analyst, Data Scientist (Insurance), Analytics Consultant
₹5–9 LPA with CS1 cleared
GLMs are the most tested area in recent years. Understand the exponential family, the link function, and the deviance, not just the mechanics.
“CS1 opened doors I did not expect. My employer at EY uses GLMs every day, and I was the only analyst in my batch who understood what was happening. That came entirely from S.MONK.”