Discrete Math Notes:
Chapter 8: Applications of Discrete Mathematics
8.10 Bernoulli trials and the binomial distribution
Bernoulli trial, an experiment with two outcomes: success and failure
Bernoulli process,the outcomes of the repeated experiments are assumed to be mutually independent and have the same probability of success and failure.
binomial distribution, distribution over the random variable defined by the number of successes in a sequence of independent Bernoulli trials
Theorem 8.10.1: Bernoulli trial probabilities, the probability of exactly k successes in a sequence of n independent Bernoulli trials, with probability of success p and probability of failure q = 1 - p is
overview:
A Bernoulli trial is a test that has two possible outcomes: success or failure. The outcomes of repeated Bernoulli trials are supposed to be mutually independent and have the same probability of success and failure in a Bernoulli process, which is a succession of independent Bernoulli trials. Bernoulli processes are used to model a variety of key computer science events. A Bernoulli process is widely used to mimic faults in transmitting bits over a communication channel, for example. A success is when a bit is communicated correctly, while a failure is when the bit is flipped during transmission. The binomial distribution is the probability distribution over a random variable determined by the number of successes in a series of independent Bernoulli trials.