Question

11. using the probability listed below

x 0 1 2 3 4

p(x) 0.10 0.26 0.30 0.24 0.10

a. find the mean, variance and standard deviation

b. find p(x is no more than 3)

c. find p(x is at least 2)

d. find p(x<2 or x >2)

e. find p(x is less than 3)

Answer #1

11)

Solution :

x | P(x) | x * P(x) |
x^{2} * P(x) |

0 | 0.1 | 0 | 0 |

1 | 0.26 | 0.26 | 0.26 |

2 | 0.3 | 0.6 | 1.2 |

3 | 0.24 | 0.72 | 2.16 |

4 | 0.1 | 0.4 | 1.6 |

Sum | 1 | 1.98 | 5.22 |

(a)

Mean = = X * P(X) = 1.98

variance = X
^{2} * P(X) -
^{2} = 5.22 - 1.98^{2} = 1.2996

Standard deviation = = 1.14

(b)

P(x is no more than 3) = 0.10 + 0.26 + 0.30 + 0.24 = 0.90

(c)

(x is at least 2) = 0.30 + 0.24 + 0.10 = 0.64

(d)

(x<2 or x >2) = 0.10 + 0.26 + 0.24 + 0.10 = 0.70

(e)

(x is less than 3) = 0.10 + 0.26 + 0.30 = 0.66

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