Multinomial Distribution Calculator ·

21 Jun 2024, 00:00

Multinomial Distribution Calculator

Given a multinomial distribution with xi = {5,2,1} and θi = {0.5,0.3,0.2}, calculate the probability ƒ(5,2,1;8,0.5,0.3,0.2)

The multinomial distribution formula is below:

ƒ(x0!·x1!·x2;n,θ0,θ1,θ2) =	n!(θ0x0·θ1x1·θ2x2)
	x0!·x1!·x2

Calculate n:

n = 5 + 2 + 1
n = 8

Plugging in our numbers, we get:

ƒ(5,2,1;8,0.5,0.3,0.2) =	8!(0.55 × 0.32 × 0.21)
	5!·2!·1

ƒ(5,2,1;8,0.5,0.3,0.2) =	8!(0.03125 × 0.09 × 0.2)
	120 × 2 × 1

ƒ(5,2,1;8,0.5,0.3,0.2) =	40320(0.0005625)
	120 × 2 × 1

ƒ(5,2,1;8,0.5,0.3,0.2) =	22.68
	240

ƒ(5,2,1;8,0.5,0.3,0.2) = 0.0945

What is the Answer?

ƒ(5,2,1;8,0.5,0.3,0.2) = 0.0945

How does the Multinomial Distribution Calculator work?

Free Multinomial Distribution Calculator - Given a set of xi counts and a respective set of probabilities θi, this calculates the probability of those events occurring.
This calculator has 2 inputs.

What 1 formula is used for the Multinomial Distribution Calculator?

ƒ(x0!·x1!·x2;n,θ0,θ1,θ2) = n!(θ0x0·θ1x1·θ2x2)/x0!·x1!·x2

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Multinomial Distribution Calculator?

eventa set of outcomes of an experiment to which a probability is assigned.multinomial distributiona generalization of the binomial distribution. probabilitythe likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes

Multinomial Distribution Calculator