Given a multinomial distribution with xi = {0,2,4} and θi = {0.9,0.05,0.05}, calculate the probability ƒ(0,2,4;6,0.9,0.05,0.05)
The multinomial distribution formula is below:
| ƒ(x0!·x1!·x2;n,θ0,θ1,θ2) = | n!(θ0x0·θ1x1·θ2x2) |
| x0!·x1!·x2 |
Calculate n:
n = 0 + 2 + 4n = 6
Plugging in our numbers, we get:
| ƒ(0,2,4;6,0.9,0.05,0.05) = | 6!(0.90 × 0.052 × 0.054) |
| 0!·2!·4 |
| ƒ(0,2,4;6,0.9,0.05,0.05) = | 6!(1 × 0.0025 × 6.25E-6) |
| 1 × 2 × 24 |
| ƒ(0,2,4;6,0.9,0.05,0.05) = | 720(1.5625E-8) |
| 1 × 2 × 24 |
| ƒ(0,2,4;6,0.9,0.05,0.05) = | 1.125E-5 |
| 48 |
ƒ(0,2,4;6,0.9,0.05,0.05) = 2.34375E-7
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What is the Answer?
ƒ(0,2,4;6,0.9,0.05,0.05) = 2.34375E-7
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!·x2For more math formulas, check out our Formula Dossier
What 3 concepts are covered in the Multinomial Distribution Calculator?
- event
- a set of outcomes of an experiment to which a probability is assigned.
- multinomial distribution
- a generalization of the binomial distribution.
- probability
- the 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
