Some Important Probability Distributions

 The probability distributions are some of the model which try to find a relation between the probability of occurrence of the event along the varying the variable size. Some of the important probability distributions are

• Uniform distribution is a model which got “no preference”. In this probability distribution the chance of occurrence all the event are same. The entire event has fair probability of occurrence. This distribution is often called as the parent distribution as most of the other distributions are derived from this distribution. The distribution is given by the formula.  

  

  Where ‘a’ and ‘b’ are its extreme limits the value of the distribution at these points is almost nil. f(x) is the probability of occurrence, x being a random variable.

• Binomial distribution is a model in which the variable which has repeated outcome is analyzed. In this model the outcome from the variable will be known. In case of binomial distribution the outcome is either a success or a failure. This repeats again and again. A simple example for binomial event is tossing of the coin again and again. The outcome from this event is either heads or tails, there won’t be any other outcome, and however the event is repeated again and again to form a distribution.  The binomial distribution is given by the formula

  

  where n is the no of trials, k is the probability of success, 1-k being the probability of the occurrence of the failure.

• Poison distribution is also called as distribution of rare events. In this distribution the events which are considered never happens at the same time. If the binomial distribution limits extends to infinity then it forms poison distribution.

  

             where k is random variable, n being the no of event, k being the probability of success.

Question

• What is probability distribution?
• Explain some of the probability distribution model?