Binomial distribution, Applied Statistics

Assignment Help:

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 crprqn-r


Related Discussions:- Binomial distribution

Convenience sampling, Convenience Sampling It means a convenient sample...

Convenience Sampling It means a convenient sample is obtained by selecting convents units from the universe. Convenient sample is also known as chunk. It   means a fraction of

Regression analysis and experimental design, For many decades, there has be...

For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S

Solve the normal distribution problem, Assume that the normal distribution ...

Assume that the normal distribution applies and find the critical z value(s). A = 0.04; H1 is mean ≠ 98.6 degrees Fahrenheit. Dteremine the value of Z. Find the value of the

Determine relative frequency, A sample of college students and a separate s...

A sample of college students and a separate sample of adults aged 30-59 were surveyed regarding the amount of fruit they eat each day.  The results are shown in the histograms belo

What are the null and alternative hypotheses, Test the following claim. Id...

Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that

Testing of hypothesis, Testing of Hypothesis One objective of sampling...

Testing of Hypothesis One objective of sampling theory is Hypothesis Testing. Hypothesis testing begins by making an assumption about the population parameter. Then we gather

Factor loadings matrix, As we stated above, we start factor analysis with p...

As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem. This knowled

Graphical calculation for mode, For calculating the mode of the grouped dat...

For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.

Pneumatic actuator design matrix, Pneumatic Actuator Design Matrix: The ra...

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Standard deviation, Standard Deviation The main drawback of the deviati...

Standard Deviation The main drawback of the deviation measures of dispersion, as discussed earlier, is that the positive and negative deviations cancel out each other. Use of t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd