Question

Find the mean, variance, and standard deviation of the random variable having the probability distribution given in the following table. (Round your answers to four decimal places.)

Random variable, x |
-7 | -6 | -5 | -4 | -3 |

P(X = x) |
0.13 | 0.16 | 0.4 | 0.15 | 0.16 |

Answer #1

Solution :

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

-7 | 0.13 | -0.91 | 6.37 |

-6 | 0.16 | -0.96 | 5.76 |

-5 | 0.4 | -2 | 10 |

-4 | 0.15 | -0.6 | 2.4 |

-3 | 0.16 | -0.48 | 1.44 |

Sum | 1 | -4.95 | 25.97 |

Mean = X * P(X)

= **-4.95**

Variance

= X 2 * P(X) - 2

= 25.97 - (-4.95)2 = **1.4675**

Standard deviation =
= **1.2114**

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