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Chapter 8: The Binomial and Geometric Distributions
Transcript of Chapter 8: The Binomial and Geometric Distributions
Independent (one outcome doesn't affect another)
Number of trials is set in advance
Success on each trial (probability of success must be the same) Parameters n and p n is the number of observations
p is the probability of success of any one observation x= B(n,p) The possible values of x are the whole numbers from zero to n X is defined... Binomial Coeffiecient Where n is the number of observations and k is the number of successes What is the difference between a probability distribution function (pdf) and a cumulative distribution function (cdf)? Binomial Probability Mean and Standard Deviation of a Binomial Random Variable If a count X has the binomial distribution with number of observations n and the probability of success p, the mean and standard deviation of X are: Pdf assigns probablity to each value of X for 0,1,2... up to the value X. Cdf is the cumulative sum that adds up (x=0)+(x=1)+...(x=k). Use...
Pdf when given exact value of X. Ex: p(x=3)
Cdf when given key words such as: "at most X" and "at least X" Calculator Pdf: 2nd, vars, A Binompdf(n,p,k)
Cdf: 2nd, vars, B Binomcdf(n,p,k)
Where n is number of observations, p is the probablity, and k is number of successes. Geometric Distributions Geometric Setting Binary (success and failure)
Independent (one outcome does not affect another)
Trials required to obtain the first success
Success on each trial (probability of sucess must be the same) Key Difference Between Binomial and Geometric Setting Geometric setting counts the number of trials until an event of interest happens.
Binomials settings have a fixed set of n trials. X is Defined...
X= G(p,n) Geometric Probablity The Geometric probability that X takes any value: p(x=n)=(1-p)^n-1xP
(geometric pdf) Geometriccdf:(1-p)^n
The probability that it takes more/less than n trials to get a success.
p(x>n),p(x<n) Mean and Standard Deviation for Geometric Distribution The mean is the expected number of trials to get a success
The standard deviation of a geometric distribution is:
Calculator Geometric pdf: 2nd, vars, E, geometpdf(p,n)
Geometric cdf: 2nd, vars, F, gemometcdf(p,n) Thank You