I'm a first year undergraduate engineering student and we've got a course "Introduction to Probability Theory" which roughly covers the following topics:
addition, multiplication, marginal and conditional probability, joint probability, Baye’s theorem, random variables, probability mass function, probability distribution function, moments and moments generation function, binomial distribution, Poisson distribution, exponential distribution, Gaussian /normal distribution, gamma distribution, Chebyshev’s inequality, Schwartz inequality, q function, random process, autocorrelation, auto covariance function, stationary process, Erlang process, ergodic random process, Markov chain and transitional probability, order of Markov chain, Chapman-Kolmogorov equation, irreducible state, absorbing state, ergodoic chain, birth and death process, Markovian queuing models
It would be very helpful if someone could suggest me a good book which covers all the above topics, because I searched on the net but no book seems to cover all the topics. Also our professor didn't suggest any book as such, but it would be helpful to have one because sometimes the professor's explanations can be confusing.
As a mathematics student I've had courses on probability theory and stochastic processes, and for both of those courses used the book Probability Theory and Random Processes by Grimmet and Stirzaker. The explanations were clear, and I remember the exercises in the book to be quite challenging. At least in my experience back then, but I didn't have any previous experience with probability theory at that point.
Just had a look through the Contents, and it seems to cover pretty much all your topics (as far as I can tell from the contents).
Hope that helps.