The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .97, and the other has a reliability of .99.

a. What is the reliability of the computer?

b. A backup computer identical to the one being used will be installed to improve overall reli- ability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability.

c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .98, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.)

Cool beans is a locally owned coffee shop that competes with two large coffee chains, planeteuro and frothies. alicia, the owner, hired two students to count the number of customers that entered each of the coffee shops to estimate what percent of people who are interested in coffee are visiting each shop. after a week, the students found the following results: 589 visited cool beans, 839 visited planeteuro, and 1,290 visited frothies. the students were surprised that cool beans had 139 visits on monday which represented 59% of all people who visited one of the three coffee shops on mondays. how many people visited one of the three coffee shops during the week?

You are a manager at asda. you have been given the demand data for the past 10 weeks for swim rings for children. you decide to run multiple types of forecasting methods on the data to see which gives you the best forecast. if you were to use exponential smoothing with alpha =.8, what would be your forecast for week 22? (the forecast for week 21 was 1277.) week demand 12 1317 13 1307 14 1261 15 1258 16 1267 17 1256 18 1268 19 1277 20 1277 21 1297

Stocks a, b, and c are similar in some respects: each has an expected return of 10% and a standard deviation of 25%. stocks a and b have returns that are independent of one another; i.e., their correlation coefficient, r, equals zero. stocks a and c have returns that are negatively correlated with one another; i.e., r is less than 0. portfolio ab is a portfolio with half of its money invested in stock a and half in stock b. portfolio ac is a portfolio with half of its money invested in stock a and half invested in stock c. which of the following statements is correct? a. portfolio ab has a standard deviation that is greater than 25%.b. portfolio ac has an expected return that is less than 10%.c. portfolio ac has a standard deviation that is less than 25%.d. portfolio ab has a standard deviation that is equal to 25%.e. portfolio ac has an expected return that is greater than 25%.