Text Recommendations

[PaultheS]

(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)?