Geometric Distribution

X ~ Geo(p)

p: probability of success

The Geometric distribution is a discrete distribution used to calculate the probability that the first successful outcome occurs on a specific trial (x).

Example

Geo(0.4): The probability of a successful outcome is 0.4

Geometric Graph

Conditions

  • The trials are independent of each other
  • There are two possible outcomes; success or failure
  • The probability of success is constant

Formulae

x: the trial for which the first successful outcome occurs.

P(X = x) = p(1 - p)x-1
P(X > x) = (1 - p)x
P(X ≤ x) = 1 - (1 - p)x
E(X) =
1
p
VAR(X) =
(1 - p)
p2

Enter the parameters for the geometric distribution:

Probability of success: p

This calculator does the following

  • Displays the statistics for the defined distribution
  • Calculates the probabilities for a given value of x
  • Calculates the inverse for a given probability
  • Calculates the values for a hypothesis test given the significance level: H0, H1, the critical region, probability of a type I error and the probability of a type II error given the actual parameter.
  • Calculates the values for a hypothesis test given the critical region: H0, H1, the test size, the test power for the actual parameter or the power table if no parameter is specified.
  • Displays a table of probabilities for the distribution