Suppose that the price of Asset X at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price of X at the close of trading today is $298. Suppose further that the price of Asset Y at the close of trading yesterday was $8, its volatility was estimated as 1.5% per day, and its correlation with X was estimated as 0.8. The price of Y at the close of trading today is unchanged at $8. Update the volatility of X and Y and the correlation between X and Y using (a) The EWMA model with 0.94. (b) The GARCH(1,1) model with = 0.000002, = 0.04, and = 0.94. In practice, is the parameter likely to be the same for X and Y?

Galwaysc electronics makes two products. model a requires component a and component c. model b requires component b and component c. new versions of both models are released each year with updated versions of all components. all components are sourced overseas, and abc contracts annually for a quantity of each component before seeing that year’s demand. components are only assembled into finished products once demand for each model is known. for the coming year, alwaysc’s purchasing manner has proposed ordering 500,000 units of component a, 630,000 of component b, and 1,000,000 units of component c. her boss has asked why she has recommended purchasing so much of components a and b when alwaysc will not have enough of component c to fully use all of the inventory of a and b. what factors might the purchasing manager cite to explain her recommended order? explain your reasoning.

Suppose the number of equipment sales and service contracts that a store sold during the last six (6) months for treadmills and exercise bikes was as follows: treadmill exercise bike total sold 185 123 service contracts 67 55 the store can only sell a service contract on a new piece of equipment. of the 185 treadmills sold, 67 included a service contract and 118 did not.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.