# Formula Review

### 4.1Hypergeometric Distribution

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

### 4.2Binomial 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.

### 4.3Geometric 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 = = $1 p ( 1 p −1 ) 1 p ( 1 p −1 )$ .

### 4.4Poisson 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
.

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.

$P(x)=μxe-μx!P(x)=μxe-μx!$
Order a print copy

As an Amazon Associate we earn from qualifying purchases.