Bernoulli Distribution

X ~ B(n, p)

n: number of trials

p: probability of success

The binomial distribution is a discrete distribution used to calculate the probability of a given number of successful outcomes (x) from a fixed number of trials (n).

Example

B(4,0.4): The probability of success is 0.4 for each trial and there are 4 trials

Binomial Graph

Conditions

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

Formulae

x: The number of successful outcomes.

P(X = x) =
n!
x! (n - x)!
× px(1 - p)n-x
E(X) = np
VAR(X) = np(1 - p)

Enter the parameters for the Bernoulli 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
  • Displays a table of probabilities for the distribution