# μ, σ^{2}, Skewness & Kurtosis for n = 6 & P = 0.81

*mean*(μ),

*variance*(σ

^{2}),

*standard deviation*(σ), coefficient of skewness & coefficient of kurtosis of Binomial distribution for success

*probability*for each trial P = 0.81 from the total number of

*combinations*n = 6. The below is the Binomial distribution calculation summary for all the above parameters for n = 6 & P = 0.81.

Calculation Summary | |
---|---|

No. of finite events (n) | 6 |

Probability of success/Trial (p) | 0.81 |

Negative probability (q) | 0.19 |

Mean (μ) | 4.86 |

Variance (σ^{2}) | 0.9234 |

Standard deviation (σ) | 0.9609 |

Coefficient Skewness | -0.6452 |

Coefficient Kurtosis | 0.083 |

## Binomial Probability Distribution Workout for n = 6 & P = 0.81

The below is the example work with steps shows how to estimate the μ, σ^{2}, σ, coefficient of skewness & coefficient of kurtosis of Binomial distribution for n = 6 & P = 0.81, may help grade school students to solve the such binomial probability worksheet problems efficiently.__Workout__

step 1 Address formula, input parameters & values.

__Input parameters__

n = 6

p = 0.81

q = 1 - p = 1 - 0.81

q = 0.19

__Formula__

Mean μ = np

Variance σ^{2} = npq

Standard Deviation σ = = √npq

Coefficient Skewness = q - p/σ

Coefficient Kurtosis = 1 - 6pq/σ²

step 2 Use n, p and q values to find mean, variance and standard deviation

μ = np = 6 x 0.81

μ = 4.86

σ^{2} = npq = 6 x 0.81 x 0.19

σ^{2} = 0.9234

σ = √npq = √0.9234

σ = 0.9609

step 3 Apply the values in Coefficient Skewness formula

Coefficient Skewness = q - p/σ

= 0.19 - 0.81/0.9609

= -0.62/0.9609

= -0.6452

Coefficient Skewness = -0.6452

step 4 Apply the values in Coefficient Kurtosis formula

Coefficient Kurtosis = 1 - 6pq/σ²

= 1 - 6 x 0.81 x 0.19/0.9234

= 1 - 0.9234/0.9234

= 0.0766/0.9234

= 0.083

Coefficient Kurtosis = 0.083