TABLE OF CONTENTS There are several distributions that arise very often in communication problems. These include binomial distribution, Poisson distribution, and normal, or gaussian distribution.
A r.v. X is called a binomial r.v with parameters ( n,p) if its pmf is given by
where 0 ? p ? 1 and
which is known as the binomial coefficient. The corresponding cdf of X is
The mean and variance of the binomial r.v. X are
The binomial random variable X is an integer-valued discrete random variable associated with repeated trials of an experiment. Consider performing some experiment and observing only whether event A occurs. If A occurs, we call the experiment a success; if it does not occur ( A occurs), we call it a failure. Suppose that the probability that A occurs is P( A) = p; hence, P( A) = q = 1 ? p. We repeat this experiment n times (trials) under the following assumptions:
P( A) is constant on each trial.
The n trials are independent.
A point in the sample space is a sequence of nA's and A's. A point with kA's and n ? k A's will be assigned a probability of p k q n ? k. Thus, if X is the random variable associated with the number of times that A occurs...
