Question

The weekly demand of a slow-moving product has the probability mass function shown to the right.

Find the expected value, variance, and standard deviation of weekly demand. Type an integer or decimal, DO NOT ROUND

Demand, x | Probability, f(x) |

0 | 0.2 |

1 | 0.3 |

2 | 0.4 |

3 | 0.1 |

4 or more | 0.0 |

Answer #1

Solution:

Given that,

X | P(X) | X*P(X) | X^2*P(X) |

0 | 0.2 | 0 | 0 |

1 | 0.3 | 0.3 | 0.3 |

2 | 0.4 | 0.8 | 1.6 |

3 | 0.1 | 0.3 | 0.9 |

4 | 0 | 0 | 0 |

Sum = |
1 |
1.4 |
2.8 |

Mean :

E(X) = = X * P(X)

= **1.4**

Variance :

=
X^{2} * P(X) - ()^{2}

= 2.8 - ( 1.4 )^{2}

= **0.84**

Standard deviation:

=
X^{2} * P(X) - ()^{2}

= Variance

= 0.84

= **0.9165**

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0
2
4
6
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F(x)
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0.3
0.2
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Demand for the Company’s Products
Probability of this demand occurring
Rate of return if this demand occurs (%)
Weak
0.1
-50
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0.2
-15
Average
0.4
16
Above Average
0.2
25
Strong
0.1
60
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Demand for
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Probability of Occurrence of
Demand
Return if
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Weak
0.1
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Below
Average
0.2
-5
Average
0.4
12
Above
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0.2
21
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0.1
50
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x Subscript ixi
P(Xequals=x Subscript ixi)
x Subscript ixi
P(Xequals=x Subscript ixi)
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0.030.03
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0.2
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0.1
3
0.3
4
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