June 18, 2025.

 Probability for computer science: 
   inequalities and their bounds

This monograph provides a basic review on probability
topics for computing students.
Students in other disciplines such as engineering, 
applied mathematics and statistics, and data science 
will  also find the topics interesting.

Topics available include
(1) Briev review on probability theory,

(2) random variables and properties 
    (expectation, variance),

(3) standard distribution (and their properties),

(4) moment generating functions,

(5) probability inequalities 
    (Markov, Chebyshev, Jensen, Cauchy-Schwartz),

(6) tails of the binomial distribution,

(7) Chernoff's method, derivative concentration bounds 
and bounds on the left and right tails,

(8) Hoeffding's method, derivative concentration bounds 
and bounds on the left and right tails,

(9) a section with combinatorial equalities and 
inequalities, exponential and logarithmic inequalities 
useful in computer science,

(10) a collection of examples 
(with sample indicative solutions) on balls and bins, 
entropy function, binomial distribution,
birthday and coupon problems, hashing (hash tables), 
random graphs and matrices, randomness, 
and ramsey numbers.