**Question: **It was suggested that five is the minimum number of data points for the least likely category when constructing discrete distributions. In many cases, however, we must estimate probabilities that are extremely small or for which relatively few data are available. For example, the probability of bankruptcy for a firm is (hopefully) quite small, but it is important for both borrowers and lenders to know this small probability value. Typically, either expert opinion or proxy measures are used to determine these small probability values instead of using data, What makes us reluctant to use data to estimate small probability values?

## Maximum number of familiesSuppose further that tribe B uses twice as much water as tribe A. What is the maximum number of families of each tribe that can coexist in the valley. |

## State the definition of an algorithmState the definition of an algorithm and define specific attributes that must be possessed by an algorithm |

## What is the leaving arcConsider the tree solution for the following minimum cost network flow problem: The numbers on the tree arcs represent primal flows while numbers on the nontree |

## Population experiences exponential growthA bacterial population experiences exponential growth during a 4-day period. Assume that 200 colonies were present at the beginning of the 1st day, but by the beginning of the 3rd day, the population had grown to 335. |

## What is the optimal refactorization frequencyShow that an iteration of the revised simplex method takes longer than an iteration of the standard simplex method whenever the bases B. |

## Find the measurements of the vector bGiven the following bases in R2, and the vector b' = [5, 5], find the "measurements" of the vector b according to each basis. Hint: Graph the dual space. |

## Find the differential coefficient of the equationsThe basic rules of calculus find the differential coefficient of the equations - Using the basic rules of calculus Integrate the given problems. |

## Compute the probability that consumer uses a plastic cardVisa Card USA studied how frequently young consumers, ages 18 to 24. use plastic (debit and credit) cards in making purchases (Associated Press. January 16. |

## Develop integer optimization model-setup plants-sales depotsThe total production is 165 cars and the demand is 86 cars. Since production is more than demand, management wishes to shut down some plants if required. Develop an integer optimization model to determine where to setup plants and sales depots su.. |

## What are the values of the given parameters a and bOn a linear demand schedule quantity sold falls from 90 to 30 when price rises from £40 to £80. How much further will price have to rise for quantity sold. |

## Calculate the motel operating income for the yearA 70-room motel's average room rate is $125. Its average occupancy is 74%. Fixed costs are $1,056,000 a year and variable costs are $212,704 a year. |

## What is the advantage of reducing process variationMotorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. |

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