Probability Distributions in Statistics

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In statistics, probability distributions are very important measure which related to the random variable and statistical data. Every data patern follows a probability distribution. Continuous data follow the continuous distribution and discrete data follow the discrete distributions. According to wikipedia,

“In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.”

 
 

Probability distributions

The idea of a probability distribution exactly parallels that of a frequency distribution. Each type of distribution is based on a set of mutually exclusive and exhaustive measurement classes or class intervals. A probability distribution is thus an idealization of the way things might be if we only had all the information. It dictates what we should expect to observe in a frequency distributions, if some given state of affairs is true. Thus, we can say,

Any statement of a function associating each of a set of mutually exclusive and exhaustive classes or class intervals with its probability is called probability distribution.

A probability distribution is divided into two category. They are-

  • Discrete probability distribution
  • Continuous probability distribution 

Discrete Probability Distributions

A discrete random variable assumes each of its values or numbers with a certain probability. A probability distribution with discrete random variable is called discrete probability distribution.

There are some discrete probability distributions which are very important part of statistics are following-

Continuous Distributions

When a probability distribution contains conrinuous random variable then the distribution is called continuous probability distribution. 
Some impotant continuous probability distributions are following-

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