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Introductory Business Statistics 2e

Formula Review

Introductory Business Statistics 2eFormula Review

Formula Review

4.1 Hypergeometric Distribution

h(x) = A x N-A n-x Nnh(x)= A x N-A n-x Nn

4.2 Binomial Distribution

X ~ B(n, p) means that the discrete random variable X has a binomial probability distribution with n trials and probability of success p.

X = the number of successes in n independent trials

n = the number of independent trials

X takes on the values x = 0, 1, 2, 3, ..., n

p = the probability of a success for any trial

q = the probability of a failure for any trial

p + q = 1

q = 1 – p

The mean of X is μ = np. The standard deviation of X is σ = npq npq .

P(x)=n!x!(n-x)!·pxq(n-x)P(x)=n!x!(n-x)!·pxq(n-x)

where P(X) is the probability of X successes in n trials when the probability of a success in ANY ONE TRIAL is p.

4.3 Geometric Distribution

P(X=x)=p(1−p)x−1P(X=x)=p(1−p)x−1

X ~ G(p) means that the discrete random variable X has a geometric probability distribution with probability of success in a single trial p.

X = the number of independent trials until the first success

X takes on the values x = 1, 2, 3, ...

p = the probability of a success for any trial

q = the probability of a failure for any trial p + q = 1
q = 1 – p

The mean is μ = 1 p 1 p .

The standard deviation is σ = 1 – p p 2 1 – p p 2 = 1 p ( 1 p −1 ) 1 p ( 1 p −1 ) .

4.4 Poisson Distribution

X ~ P(μ) means that X has a Poisson probability distribution where X = the number of occurrences in the interval of interest.

X takes on the values x = 0, 1, 2, 3, ...

The mean μ or λ is typically given.

The variance is σ2 = μ, and the standard deviation is
σ =  μ σ =  μ .

The probability of having exactly xx successes in rr trials is PX=x=e-μμxx!PX=x=e-μμxx!.

When P(μ) is used to approximate a binomial distribution, μ = np where n represents the number of independent trials and p represents the probability of success in a single trial.

P(x)=μxe-μx!P(x)=μxe-μx!
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