The minimum and maximum values of the coefficient of determination r2 are, respectively,
A. 0 and 1
B. −1 and 1
C. −1 and 0
D. 0 and +∞

The following data represent a random sample of earwig density (x) and the proportion of males that have forceps (y).

Which of the following is the correlation coefficient?
A. 0.33
B. 0.17
C. 0.02
D. 0.8

Which of the following is the equation of the regression line?
A. y^=0.0072x+0.1452
B. y^=0.0072+0.1452x
C. y^=0.3319+0.1101x
D. y^=0.1101x+0.3319

Two types of flares are tested for their burning times (in min) and sample results are given below.

Part I : Test the claim that Brand X has a mean less than Brand Y. Use 0.05 significance level.

Claim:

Null Hypothesis:

Alternative Hypothesis:

Calculator Screen Name in Ti 183:

test statistics:

Pvalue/alpha conversion

decision:

Conclusion:

Part II: Construct a 95% confidence interval for U1-U2. Interpret the interval.

Confidence interval name on TI 83

Interval

Interpret.

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median giraffe height?  ft.

c. What is the Z-score for a giraffe that is 20 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 17.9 feet tall?

e. What is the probability that a randomly selected giraffe will be between 17.7 and 18.3 feet tall?

f. The 80th percentile for the height of giraffes is  ft.

The expected return of market portfolio is 10%. The standard deviation of market portfolio is 20%. Risk free interest rate is 2%. There is an investor with mean-variance utility function  Answer the following questions.

1) Calculate the optimal weight to be invested in the market portfolio for the investor with A=5 . Calculate the expected return and standard deviation of the optimal complete portfolio for the investor.

2) According to the CAPM, calculate the expected returns of two stocks (stock 1 and stock 2) with betas equal to 0.8 and 1.5 respectively.

3) Calculate the beta and expected return of the portfolio that invests 20%, 60%, and 20% on stock 1, stock 2, and the risk-free asset, respectively.

Q1) Two identical pucks collide on an air hockey table. One puck was originally at rest. If the incoming puck has a speed of 6.50 m/s and scatters to an angle of 30.0º,what is the speed of the second puck after the collision?

(You may use the result that θ₁−θ₂=90º for elastic collisions of objects that have identical masses.)

Q2)A block of mass m = 3.0 kg, moving on a frictionless surface with a speed 2.9 m/s makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.0 kg block recoils with a speed of 0.8 m/s. In Fig. 1, the mass M (in kg) is closest to:

For a three-period binomial model for modeling the price of a stock, you are given:

1. The current price of the stock is 125.
2. The length of each period is one year.
3. u = 1.2, where u is one plus the rate of capital gain on the stock if the price goes up.
4. d = 0.8, where d is one plus the rate of capital loss on the stock if the price goes down.
5. The continuously compounded risk-free interest rate is 6%.
6. The price of a three-year $90-strike European put option is $0.89.

Calculate the price of a three-year $100-strike European put option.

1. 1.23

2. 1.49

3. 1.78

4. 2.01

5. 2.48

Please provide full explanation

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median giraffe height? ft.

c. What is the Z-score for a giraffe that is 21 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 18.6 feet tall?

e. What is the probability that a randomly selected giraffe will be between 17.3 and 18.3 feet tall? f. The 75th percentile for the height of giraffes is ft.

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market’s average return was 15%. Performance is measured using an index model regression on excess returns.

a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)

b. Which stock is the best choice under the following circumstances?

The preparations of two aqueous solutions are described in the table below. For each solution, write the chemical formulas of the major species present at equilibrium. You can leave out water itself.

Write the chemical formulas of the species that will act as acids in the 'acids' row, the formulas of the species that will act as bases in the 'bases' row, and the formulas of the species that will act as neither acids nor bases in the 'other' row.

You will find it useful to keep in mind that

NH3

is a weak base.

A gas turbine unit has a pressure ratio of 5/1 and a maximum cycle temperature of 550⁰C. The turbine drives the compressor and an electric generator., the mechanical efficiency of the drive being 97%. The ambient temperature is 20⁰C and the isentropic efficiencies of the compressor and turbine are 0.8 and 0.83 respectively.

Calculate the power output in kilowatts for an airflow of 15kg/s. Calculate also the thermal efficiency and the work ratio. Neglect changes in kinetic energy, and the loss of pressure in the combustion chamber.

Take c_p = 1.005 kJ/kg K and ɣ=1.4 for the compression process, and take c_p = 1.15 kJ/kg K and ɣ=1.333 for all combustion and expansion processes.