Simulate 10 bernoulli trials with a success probability of 0.45.

The Bernoulli Trial formula is p

Trial # | Success/Failure | Math Work | Math Work II | Probability |
---|---|---|---|---|

1 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

2 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

3 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

4 | Success | 0.45^{1}0.55^{(1 - 1)} | 0.45 x 1 | 0.45 |

5 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

6 | Success | 0.45^{1}0.55^{(1 - 1)} | 0.45 x 1 | 0.45 |

7 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

8 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

9 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

10 | Failure | 0.45^{0}0.55^{(1 - 0)} | 1 x 0.55 | 0.55 |

Given your success probability of 0.45, we would have expected 0.45 x 10 = 4.5 successes

Our actual results were 2 successes and 8 failures

The median of the bernoulli trial works as follows:

- If q > p, 0
- If q = p, 0.5
- If q < p, 1

Since q > p, 0.55 > 0.45, then our median is 0

Variance σ

Variance σ

Variance σ

Skewness = | q - p |

√pq |

Skewness = | 0.55 - 0.45 |

√(0.45)(0.55) |

Skewness = | 0.1 |

√0.2475 |

Skewness = | 0.1 |

0.31 |

Skewness =

Kurtosis = | 1 - 6pq |

√pq |

Kurtosis = | 1 - 6(0.45)(0.55) |

(0.45)(0.55) |

Kurtosis = | 1 - 6(0.2475) |

0.2475 |

Kurtosis = | 1 - 1.485 |

0.2475 |

Kurtosis = | -0.485 |

0.2475 |

Kurtosis =

Entropy = -qLn(q) - pLn(p)

Entropy = -(0.55)Ln(0.55) - 0.45Ln(0.45)

Entropy = -(0.55)(-0.62) - 0.45(-0.77)

Entropy = -(-0.59) - -0.

Entropy =