There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

(a) Determine the pmf of T_o = X₁ + X₂.

(b) Calculate μ_To.
μ_To =

How does it relate to μ, the population mean?
μ_To =  · μ

(c) Calculate σ_To².

How does it relate to σ², the population variance?
σ_To² =  · σ²

(d) Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

(e) Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

A scientist is studying the relationship between x = inches of annual rainfall and y = inches of shoreline erosion. One study reported the following data. Use the following information to solve the problem by hand, then use SPSS output to verify your answers. .

X         30        25        90        60        50        35       75        110      45        80

Y         0.3       0.2       5.0       3.0       2.0       0.5       4.0       6.0       1.5       4.0

a. What is the equation of the estimated regression line?

= ______________

b. Plot the data and graph the line. Does the line appear to provide a good fit to the data points?

c. Use the least-squares line to predict the value of y when x =39

d. Fill in the missing entries in the SPSS analysis of variance table

Source             DF                   SS                    MS                  F                      P

Regression       1                      37.938

Error                ____                _____              0.058               ____________

e) Is the simple linear regression model useful for predicting erosion from a given amount of rainfall?

f) What is the p-value?

g) A linear relationship ______________ exist between x and y.

h) The simple linear regression model ______________ useful for predicting erosion from a given amount of rainfall.

i) What is the coefficient of determination.(r-squared) or r?

j) Interpret the coefficient (r-squared) of determination.

A global equity manager is assigned to select stocks from a universe of large stocks throughout the world. The manager will be evaluated by comparing her returns to the return on the MSCI World Market Portfolio, but she is free to hold stocks from various countries in whatever proportions she finds desirable. Results for a given month are contained in the following table:

a. Calculate the total value added of all the manager’s decisions this period. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

b. Calculate the value added (or subtracted) by her country allocation decisions. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. Calculate the value added from her stock selection ability within countries. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

Deleon Inc. is preparing its annual budgets for the year ending December 31, 2020. Accounting assistants furnish the data shown below.

An accounting assistant has prepared the detailed manufacturing overhead budget and the selling and administrative expense budget. The latter shows selling expenses of $664,000 for product JB 50 and $365,000 for product JB 60, and administrative expenses of $545,000 for product JB 50 and $345,000 for product JB 60. Interest expense is $150,000 (not allocated to products). Income taxes are expected to be 30%

Complete a Budgeted Income Statement

Apple is considering marketing one of two new smartphones for the coming holiday season: iPhone 8 and iPhone X. Estimated profits in total USD under high, medium, and low demand are as follows:

There is concern that profitability will be affected by a Google's introduction of the Pixel 2 smartphone viewed as similar to the iPhone 8. Estimated profits in total USD with and without competition are as follows:

a. Develop a decision tree for the Apple problem.

b. For planning, Apple believes there is a 0.99 probability that its competitor will produce a new smartphone similar to the iPhone 8. Given this probability of competition, the director of planning in Cupertino recommends spending the ad dollars and heavily marketing the iPhone X smartphone. Using expected value, what is your recommended decision?

c. Show a risk profile for your recommendation.

d. Use sensitivity analysis to determine what the probability of competition for iPhone 8 would have to be for you to change your recommended decision alternative.

1. **A crate with a mass of 45 kg is suspended from a massless rope that runs vertically upward over a light pulley. The other end of the rope is connected to a 35 kg crate, which lies on a tabletop. The coefficients of the kinetic friction and the static friction between the crate and the surface are 0.3 and 0.5 respectively. An applied force, F, pulls the 35 kg crate to the right.

1. In the first case, the applied force is just sufficient to keep the crates from sliding. Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale.
2. How much force would need to be applied in this first case?
3. In the second case, the 35 kg crate is sliding to the right with a constant velocity. Draw clearly labeled free-body diagrams for each crate including all forces drawn to scale.
4. How much force would need to be applied in this second case?
5. In the third case, the 35 kg crate moves to the right at a constant acceleration of 0.5 m/s². Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale. In this instance, draw the direction of acceleration next to each diagram.
6. How much force would need to be applied in the third case.

A cylinder of 10-m-high, and a cross-sectional area of 0.1 m2 , has a piston (that is free to move) assumed to have negligible mass and thickness (see Figure 1(a)). Above the piston there is a liquid that is incompressible (constant density and volume) with ρliquid = 1000 kg/m3 . Below the piston there is air at 300 K, with a volume of 0.3 m3 . Assume air is an ideal gas (Ru =8.314 J.mol-1 .K-1 ; Mair = 28.9628 g/mol) Use P0 = 101.325 kPa and g = 9.807 m/s2 Find the following: a- The mass (in kg) of the liquid in the cylinder. b- The initial pressure of the air compartment. c- The initial mass of air (in kg). d- The initial internal energy of air. Another negligible mass and thickness piston is placed on top of the cylinder (see Figure 1b) and pushed down by 0.1 m to compress the air. The process is isothermal. The liquid is incompressible (its volume and phase do not change). Calculate: e- The final volume of air. f- The final temperature of air when thermal equilibrium is obtained. g- The final pressure of air. h- Does the internal energy of air change? i- The boundary work used to lower the piston located on top of the air. j- The total heat transfer outside of the piston from the air compartment.

. A bike shop is selling a fashionable newly designed folding bike. The shop is now considering how many of them to order for the coming season. The supplier requires that orders for the bikes must be placed in quantities of 25. The cost per bike is $820, $790, $750 and $700 for an order of 25, 50, 75 and 100 respectively. The bikes will be sold for $1,200 each. Since there will be a new design for folding bikes next season and there is no spare storage space in the store, any bikes left over at the end of this season will have to be sold at a low price of $450 each to another bike shop. However, if the shop runs out of bikes during the season, it will suffer a loss of goodwill among its customers. The shop estimates this goodwill loss to $60 per customer who is not able to buy a bike. From past experience, the shop estimates that the demand for folding bikes this coming season will be 25, 50, 75 and 100 bikes with probabilities of 0.4, 0.3, 0.2 and 0.1 respectively.

(a) Construct the payoff table for the above situation.

(b) Which alternative should be chosen using each of the maximax, maximin, minimax regret, Hurwicz (take α = 0.6), equal likelihood, expected value, and expected opportunity loss criteria?

(c) Find the expected value of perfect information.

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)