# Best book for probability [duplicate]

I have done my masters in Statistics and am well acquainted with probability, though I am out of touch for last few years. Currently I am preparing for an exam which has a paper for probability and the syllabus is given below. I would prefer to follow a single book and make my own notes from it. I don't need over simplified starters guide kind of thing. I would prefer some of the classical books on the subject. I used to follow William Feller in my college days but am not sure if it covers everything in this syllabus (I don't have a copy with me right now). Thanks in advance for all your suggestions.

## Syllabus

• Sample space and events
• probability measure and probability space
• random variable as a measurable function
• distribution function of a random variable
• discrete and continuous-type random variable
• probability mass function
• probability density function
• vector-valued random variable
• marginal and conditional distributions
• stochastic independence of events and of random variables
• expectation and moments of a random variable
• conditional expectation
• convergence of a sequence of random variable in distribution, in probability, in p-th mean and almost everywhere, their criteria and inter-relations
• Chebyshev's inequality and Khintchine's weak law of large numbers
• strong law of large numbers and Kolmogoroff's theorems
• probability generating function, moment generating function, characteristic function, inversion theorem
• Linderberg and Levy forms of central limit theorem
• standard discrete and continuous probability distributions.

## merged by Tim♦Aug 30 '17 at 8:43

This question was merged with Book recommendations for probability because it is an exact duplicate of that question.

• I agree that this is a duplicate to previous questions. I also first learned advanced probability out of Feller's two volume series. – Michael Chernick Mar 27 '17 at 12:23