A First Course in Probability
A First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
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Axioms of Probability
Conditional Probability and Independence
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approximately assume ball selected binomial random variable cards central limit theorem Chebyshev's inequality compute conditional probability Consider continuous random variable coupons defined denote the event denote the number desired probability dice discrete random variable distribution function distribution with parameters equal EXAMPLE expected number expected value exponential random variable Find the expected Find the probability flips follows given Hence Hint independent trials inequality joint density function lands on heads large numbers least Let X denote nonnegative normal distribution normal random variable number of successes obtain occur pair percent permutation player Poisson random variable possible outcomes prob probability density function probability mass function problem proof Proposition random number random vari randomly chosen red balls result sample space sequence Show simulating Solution standard normal random Suppose tion uniformly distributed Var(A variable with mean variable with parameters white balls wins yields