STAT 2004, Week 9: Bernoulli and Binomial Distribution
STAT 2004, Week 9: Bernoulli and Binomial Distribution STAT 2004
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This 2 page Class Notes was uploaded by Mara DePena on Saturday March 26, 2016. The Class Notes belongs to STAT 2004 at Virginia Polytechnic Institute and State University taught by Metzger in Spring 2016. Since its upload, it has received 19 views. For similar materials see Introductory Statistics in Statistics at Virginia Polytechnic Institute and State University.
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Date Created: 03/26/16
STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0. Probability of success is represented by a p. For a Bernoulli random variable. o X ~ Bernoulli (p) o The expectation of a Bernoulli distribution = the probability of success. (E[X]=p) o Variance [X] = p (1-p) o SD [X] = the square root of the variance Categorical nominal: o You can put the number of successes and failures into a bar plot. BINOMIAL DISTRIBUTION 0 1 When you choose more than one observation from a Bernoulli distribution, that is a binomial distribution. Y ~ Binomial (n, p), with Y being a random variable, n being the number of observations and p being the probability. o E[Y]= n x p o V[Y]= n x p x (1-p) Ex: Randomly select 3 VT students. What is the probability that 2/3 are freshmen? o T ~ Binomial (3, .25) .25 is the probability and individual is a freshman, assuming the four classes are divided equally throughout the student population. o (.25) ( .75) x 3 = 14.1% The probability of a student being a freshman is raised to the number of freshmen. The probability of a student being from another class is raised to the number of students from another class. This is multiplied by the number of combinations: 3 in this case. In order to determine the number of combinations, you need a calculator. o TI-30: Type in the number of people total, click PROB, click nCr, hit enter, then type in the number you are choosing from the total number o TI-84 Type in the number of people total, click MATH, click PROB, click nCr, hit enter, then type in the number you are choosing from the total number If a question asks for the probability of “at most __ out of __,” you must calculate all three probabilities and add them together. If a questions asks for the probability of “at least __ out of ___,” you could add all the probabilities, or take the probability of the opposite. You can change a binomial distribution into a normal curve as well. o Say X ~ Binomial (50, .9) Multiple 50 and .9 together for the mean value. Then, find the variance of the binomial distribution to find the standard deviation. You now have the two values for the normal curve. N ~ (45, 2.12) You can use this to find the z-score and use your chart to find the proabability.
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