## Answers

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

0 | 0.0323 | 0.0000 | 0.0000 |

9 | 0.0048 | 0.0435 | 0.3919 |

74 | 0.0006 | 0.0477 | 3.5329 |

304 | 0.0002 | 0.0490 | 14.9058 |

1279 | 0.0001 | 0.0825 | 105.5381 |

2699 | 0.0000 | 0.0871 | 234.9871 |

-1 | 0.9620 | -0.9620 | 0.9620 |

total | -0.6521 | 360.3179 | |

E(x) =μ= | ΣxP(x) = | -0.6521 | |

E(x^{2}) = | Σx^{2}P(x) = | 360.3179 | |

Var(x)=σ^{2} = | E(x^{2})-(E(x))^{2}= | 359.8927 | |

std deviation= | σ= √σ^{2} = | 18.9708 |

1)

expected profit = **-0.6521**

2)

standard deviation =**18.9708**

3)

here this is binomial distribution with parameter n=11 and p=1/5

probability = | P(3<=X<=6)= | ∑_{x=x1}^{x2 } (_{n}C_{x})p^{x}(1−p)^{(n-x) } = | 0.3806 |

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