PaultheS
03-17-2005, 05:26 PM
(Cross posted on Books & Software)
I'm looking to take the first actuarial science exam (Probability) this Spring and I'd like to get some books to study for it. The topics on the exam are as follows:
General Probability
- Set functions including set notation and basic elements of probability
- Mutually exclusive events
- Addition and multiplication rules
- Independence of events
- Combinatorial probability
- Conditional probability
- Law of total probability
- Bayes’ Theorem
Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal, gamma, Weibull, and normal).
- Probability functions and probability density functions
- Cumulative distribution functions
- Mode, median, percentiles, and moments
- Variance and measures of dispersion
- Moment generating functions
- Transformations
Multivariate probability distributions (including the bivariate normal)
- Joint probability functions and joint probability density functions
- Joint cumulative distribution functions
- Central Limit Theorem
- Conditional and marginal probability distributions
- Moments for joint, conditional, and marginal probability distributions
- Joint moment generating functions
- Variance and measures of dispersion for conditional and marginal probability distributions
- Covariance and correlation coefficients
- Transformations and order statistics
- Probabilities and moments for linear combinations of independent random variables
Note that the emphasis is on applying these concepts in a risk management context. Can anyone recommend a good text or texts that cover/s all of these topics well (and hopefully more)?
I'm looking to take the first actuarial science exam (Probability) this Spring and I'd like to get some books to study for it. The topics on the exam are as follows:
General Probability
- Set functions including set notation and basic elements of probability
- Mutually exclusive events
- Addition and multiplication rules
- Independence of events
- Combinatorial probability
- Conditional probability
- Law of total probability
- Bayes’ Theorem
Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal, gamma, Weibull, and normal).
- Probability functions and probability density functions
- Cumulative distribution functions
- Mode, median, percentiles, and moments
- Variance and measures of dispersion
- Moment generating functions
- Transformations
Multivariate probability distributions (including the bivariate normal)
- Joint probability functions and joint probability density functions
- Joint cumulative distribution functions
- Central Limit Theorem
- Conditional and marginal probability distributions
- Moments for joint, conditional, and marginal probability distributions
- Joint moment generating functions
- Variance and measures of dispersion for conditional and marginal probability distributions
- Covariance and correlation coefficients
- Transformations and order statistics
- Probabilities and moments for linear combinations of independent random variables
Note that the emphasis is on applying these concepts in a risk management context. Can anyone recommend a good text or texts that cover/s all of these topics well (and hopefully more)?