# 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*)=Ã—^{n}C_{r}*p*(1 -^{r}*p*)^{n }^{- r},*r*= 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 - A continuous random variable
*x*is said to follow Normal distribution if it has a probability density function - 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 - If the probability function of a continuous random variable
*x*is*p*(*x*) 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 by - A continuous probability distribution which has the following probability density function is called
*f*-distribution