Question

Find the mean, variance and standard deviation for the probability distribution given below:

X | -2 | 3 | 12 | 9 |

P(X) | 0.556 | 0.109 | 0.206 | 0.129 |

Round to three decimal places.

A. Mean =

B. Variance =

C. Standard Deviation =

Answer #1

Solution:

x | P(x) | x * P(x) | x2 * P(x) |

-2 | 0.556 | -1.112 | 2.224 |

3 | 0.109 | 0.327 | 0.981 |

12 | 0.206 | 2.472 | 29.664 |

9 | 0.129 | 1.161 | 10.449 |

Sum | 1 | 2.848 | 43.318 |

Mean = X * P(X)

= **2.848**

Variance

= X 2 * P(X) - 2

= 43.318 - (2.848)2 = **35.2069**

Standard deviation =
= **5.934**

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