Using a Poisson distribution with a probability of success of 0.4, calculate the Probability of having exactly 0 successes in 10 tries. Start with the Poisson Distribution formula below:

P(k; λ) = | λ^{k} |

e^{λ}k! |

λ = p * n

λ = 0.4 * 10

λ = 4

k! = 0!

0! =

0! = 1

P(k; λ) = | λ^{k} | |

e^{λ}k! |

P(0; 4) = | 4^{0} | |

2.718281828^{4}(0!) |

P(0; 4) = | 1 | |

54.598150033144 * 1 |

P(0; 4) = | 1 | |

54.598150033144 |

P(0; 4) = **0.0183**

Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

This calculator has 4 inputs.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

This calculator has 4 inputs.

- distribution
- value range for a variable
- event
- a set of outcomes of an experiment to which a probability is assigned.
- factorial
- The product of an integer and all the integers below it
- mean
- A statistical measurement also known as the average
- moment
- a function are quantitative measures related to the shape of the functions graph
- poisson distribution
- a discrete probability distribution that is used to show how many times an event is likely to occur over a specified period.
- 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 - standard deviation
- a measure of the amount of variation or dispersion of a set of values. The square root of variance
- variance
- How far a set of random numbers are spead out from the mean

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In the poisson distribution, mean and variance = λ

μ = λ

μ =

σ

σ

σ = √σ

σ = √4

σ =

Skewness = | 1 |

√λ |

Skewness = | 1 |

√4 |

Skewness = | 1 |

2 |

Skewness =

Kurtosis = | 1 |

λ |

Kurtosis = | 1 |

4 |

Kurtosis =