Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH, HT, TH, and TT. Now, let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0, 1, or 2, so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range, but are actually binomial such as yes/no. This is used frequently in quality control, reliability, survey sampling, and other corporate and industrial situations. This type of distribution can measure levels of performance only if the results can be placed into a binomial order, such as with a point estimate where only one number is relied upon.
For example, if you measure whether unit X had exceeded its monthly energy limits usage and is interested in a yes or no answer. This type of distribution gives the probability of an exact number of successes in independent trials (n), when the probability of success (p) on single trial is a constant. The probability of getting exactly r success in n trials, with the probability of success on a single trial being p is: P(r) (r successes in n trials) = nCr . pr . (1- p)(n-r) = n! / [r!(n-r)!] . [pr . (1- p)(n-r)]. Continuous Distributions: -Continuous probability functions are defined for an infinite number of points over a continuous interval. .