Calculate the mean and variance for the random variable in Exercise 3-35.

3-35. The following table shows the typical depth (rounded to the nearest foot) for nonfailed wells in geological formations in Baltimore County (The Journal of Data Science, 2009, Vol. 7, pp. 111–127).

Geological Formation Group |
Number of Nonfailed Wells |
Nonfailed Well Depth |

Gneiss |
1,515 |
255 |

Granite |
26 |
218 |

Loch Raven Schist |
3,290 |
317 |

Mafic |
349 |
231 |

Marble |
280 |
267 |

Prettyboy Schist |
1,343 |
255 |

Other schists |
887 |
267 |

Serpentine |
36 |
217 |

Total |
7,726 |
2,027 |

Calculate the probability mass function of depth for nonfailed

wells from the table.

Solution:

Step 1 of 3:

The data about the typical depth for non failed wells in Baltimore Country is given.

Geological Formation Group |
Number of non failed Wells |
Non failed Well Depth |

Gnesis |
1,515 |
255 |

Granite |
26 |
218 |

Loch Raven Schist |
3,290 |
317 |

Mafic |
349 |
231 |

Marble |
280 |
267 |

Prettyboy Schist |
1,343 |
255 |

Other Schist |
887 |
267 |

Serpentine |
36 |
217 |

Total |
7,726 |
2,027 |

We have to find the mean and variance of the random variable.