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Summary

  • A distribution is said to be discrete if the values taken by the corresponding random variables are fixed.
  • A distribution is said to be continuous if the random variable takes any value, fractional or integral, in a specified interval.
  • A binomial distribution is applied in a situation where a random experiment having only two mutually exclusive outcomes, i.e., positive or negative. Success or failure, etc., is repeated a fixed number of times.
  • A discrete random variable x is said to follow binomial distribution if its probability mass function is given by p(x = r)nCr × pr (1 - p)n rr = 0, 1, 2,..., n.
  • Poisson distribution is a limiting form of binomial distribution. Poisson distribution is applied in situations where the probability of success is very low and that of failure is very high in a small interval of time.
  • A random variable X is said to follow Poisson distribution if its probability mass function is given by Description: 70032.png
  • A continuous random variable x is said to follow Normal distribution if it has a probability density function Description: 70039.png
  • Standard normal distribution is very similar to a normal distribution. In this case, the mean, median and mode are all equal to zero and in the case of standard deviation it is equal to 1.
  • A continuous random variable z is said to follow Normal distribution if it has a probability density function Description: 70050.png
  • If the probability function of a continuous random variable x is p(xDescription: 70061.png then it is said to follow Chi-square distribution.
  • If a continuous random variable t follows t-distribution with n degrees of freedom, then its probability density function is given byDescription: 70077.png
  • A continuous probability distribution which has the following probability density function is called f-distribution Description: 70083.png




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