Binomial Distribution

Binomial distribution  was discovered by swiss mathematician James  Bernonulli, so this distribution is called as Bernoulli distribution also, this is a discrete frequency distribution.

Assumptions of a binomial Distribution

1.       The random experiment  is performed repeatedly with a fixed  and finite  number of trials. N is denoted by number of trials.

2.      There are two mutually exclusive  possible outcomes on each trial which  are known as success and failure success is  denoted by  whereas failure is denoted  by q, and p+q = 1  or  q=1-p1.

3.      The outcomes  of any given  trial does not affect the outcomes  on subsequent  trials means the trials  are independent.

4.      The probability  of success  and failure (p&q)  remains constant from trial to  trial. If in any distribution the p& q  does not remain constant    that distribution cannot be a binomial distribution, For  example  the probability  of getting  head  must remain  the same in each  toss i.e. ½  similarly  the probability  of drawing  4 balls  from a bag containing  6  red  and 10 white balls  does not  change in successive  draws  with replacement, hence it  will be called  as binomial distribution .But in contrary  to this, if balls  are not replaced  after  each trail then it will not be a binomial  distribution.

5.      If all above  assumptions are satisfied , the probability of exactly  r successes in  n trials is given by

6.      P(n=r)=ⁿ c_rp^rq^n-r

Posted Date: 9/27/2012 7:01:55 AM | Location : United States

Ask an Expert

Related Discussions:- Binomial distribution, Assignment Help, Ask Question on Binomial distribution, Get Answer, Expert's Help, Binomial distribution Discussions

Write discussion on Binomial distribution
Your posts are moderated

Write your message here..

Related Questions

Index number of price for paasche’s method, Construct index numbers of pri... Construct index numbers of price for the following data by applying: i)      Laspeyre’s method ii)     Paasche’s method iii)    Fisher’s Ideal Index number

Confirmatory factor analysis, Confirmatory factor analysis (CFA) seeks to d... Confirmatory factor analysis (CFA) seeks to determine whether the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the ba

Calculate the maximum weight of the engine, Determine the maximum weight in... Determine the maximum weight in kN to one decimal point (1 DP) of the engine that can be supported without exceeding the tension given in  Parameter 1 (P1) in chain AB or 1.1 x P1

Find the unbiased estimators for mean and variance matrix, Is the random ve... Is the random vector (Trunk Space, Length, Turning diameter) of US car normally distributed? Why? If yes, find the unbiased estimators for the mean and variance matrix of (Trunk Sp

Coefficient of variation, Coefficient of Variation The standard dev... Coefficient of Variation The standard deviation discussed above is an absolute measure of dispersion. The corresponding relative measure is known as the coefficient of vari

Che, Chebychev inequality Chebychev inequality

Cluster analysis, Cluster Analysis could be also represented more formally ... Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr

Effect in frequency domain, A) The three images shown below were blurred us... A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le_ lower part of (a) and (c) are blurred, but a c

TIME SERIES,

#title., Features of index numbers Features of index numbers