Maths and Computing:

X ~ B(n, p)

The binomial distribution is a discrete distribution used to calculate the probability of a given number of successful outcomes (x) out of 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

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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

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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 binomial distribution:

Number of trials: n
Probability of success: p

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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