Bernoulli distribution, discrete probability

A single coin is an example of a Bernoulli" distribution. This probability distribution limits values of the random variable to exactly two discrete values, one with probability p, and the other with the probability (1-p). For the coin, the two values are heads p, and tails (1-p), where p = 0.5 for a fair coin. 

A discrete distribution function assigns probabilities to several separate outcomes of an experiment. By this law, the total probability equal to number one is distributed to individual random variable values. A random variable is fully defined when its probability distribution is given. The probability distribution of a discrete random variable shows probabilities of obtaining discrete-interrupted random variable values. It is a step function where the probability changes only at discrete values of the random variable. The Bernoulli distribution assigns probability to two discrete outcomes (heads or tails on or off 1 or 0, etc.). Hence it is a discrete distribution. 

The binomial distribution gives the discrete probability distribution of obtaining n successes out of N Bernoulli trials. The result of each Bernoulli trial is true with probability p and false with probability q = I- p (Figure D.l). 

The Binomial distribution, also known as Bernoulli distribution, belongs to the discrete distribution. The specific feature of the binomial distribution is that it can accept only 2 values. This means that a component failure is present x = 0 or is not present X= 1. The probability of exactly x successes is given by this formula ... 

The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is n x repeated Bernoulli trial. The binomial distribution is the basis for the popular binomial test of statistical significance. 

---