Suppose you have multiple independent Bernoulli random variables, [tex]X_1,X_2,...,X_n[/tex], with respective probabilities of success [tex]p_1,p_2,...,p_n[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

So [tex]E(X_i)=p_i[/tex], and [tex]E(X_i+X_j)=E(X_i)+E(X_j)[/tex]. Also, [tex]\text{var}(X_i)=p\cdot (1-p)[/tex], and [tex]\text{var}(X_i+X_j)=\text{var}(X_i)+\text{var}(X_j)[/tex]. (Though correct me if any of that is wrong.)

I'm trying to figure out the similar formulae for skewness and kurtosis. Since skewness of [tex]X_i[/tex] is given by [tex]\tfrac{(1-p_i)-p_i}{\sqrt{p_i\cdot(1-p_i)}}[/tex], how would you calculate the skewness of [tex]X_i+X_j[/tex]? And for kurtosis of [tex]X_i+X_j[/tex]?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Skewness and Kurtosis of Bernoulli Distributions

Loading...

Similar Threads - Skewness Kurtosis Bernoulli | Date |
---|---|

Skewness, Kurtosis applied | Jun 5, 2014 |

Skewness and kurtosis | May 12, 2014 |

Uncertainty of Sample skew and kurtosis | Oct 17, 2013 |

Skewness or Kurtosis Problem? | Nov 25, 2007 |

Skew & Kurtosis: Weighting Signficance | May 20, 2007 |

**Physics Forums - The Fusion of Science and Community**