3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and Y1...Xn independent of each other. Assume that the common population SD σ is known but the two means are not. Consider testing the hypothesis null: μx = μy vs alternative: μx ≠ μy.

d. Assume σ=1 and n=20. How large must δ be for the size 0.01 test to have power at least 0.99?

e. Assume σ=1and δ=0.2. How large must n be for the size 0.01 test to have power at least 0.99?

Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500 was +27% (that is, 0.27) and its standard deviation is 20% (that is, 0.2). What is the probability that a stock in the S&P 500 gained 30% or more last year?

(a) 0.0668 (i.e., 6.68%)
(b) 0.4404 (i.e., 44.04%)
(c) 0.5596 (i.e., 55.96%)
(d) 0.9332 (i.e., 93.32%)

What is the probability that a stock in the S&P 500 lost 10% or more last year?

(a) 0.1814 (i.e., 18.14%)
(b) 0.0082 (i.e., 0.82%)
(c) 0.0322 (i.e., 3.22%)
(d) 0.0743 (i.e., 7.43%)

Given the following information,

a) What are the expected returns for stock A and B, respectively?

b) What is the standard deviation/risk for stock A? List the formula and input the number, no calculation needed.

c) What is the portfolio return given that you have $10,000 and allocate $3,000 in stock A and the rest in stock B? List the formula and input the number, no calculation needed.

d) The principle of diversification states that as the number of stocks under the portfolio increases, the portfolio risk more likely A) increases or B) decreases?

Suppose you plan to take a survey of math students asked about their overall grades. 22 students were surveyed, and it was found that the average GPA of the 22 sampled students was a 3.2, with a standard deviation of 0.9 points. Suppose you want to re-sample the population to reduce the margin of error. If you plan to calculate a 90% confidence interval for the true mean GPA of math students, how many samples would be necessary to reduce the margin of error to 0.2 points? Round your answer to the nearest whole number, and remember it's always better to sample too many rather than not enough.

A 240 V DC shunt motor draws 40 A while driving a constant torque load. The armature resistance is Ra = 0.2 Ω, the field resistance is Rf = 240 Ω and machine constant is Ka = 120. The part of magnetization characteristic (field flux versus field current) related to the question is:

If (A) :      0.70 0.80 0.86 0.90 1.00 1.10 1.20 1.30 1.40

ϕ (mWb) : 5.80 6.30 6.59 6.70 7.20 7.60 7.96 8.20 8.45

The constant rotational loss is 240 W and the armature reaction is neglected. Find

a. the internal torque developed by the motor

b. speed    

c. efficiency    

A laboratory scale experiment has been planned to
study the vortex shedding induced loading on a
structural member. For doing this, the accurate
measurements of flow velocity and vortex shedding
frequency is of prime importance. The member is
placed vertically across the flow having mean flow
velocity of 50 m/s. The diameter of the member is 5
cm. If the Strouhal number is 0.2, determine the
following:

appropriate sensor type for measurements and its
characteristics ?

vortex shedding frequency?

sampling frequency required to resolve the
frequency content?

sampling frequency necessary to reconstruct the
waveform and amplitude?

would you filter the signal before acquisition, if yes
then mention reasons?

Consider an economy with the following components of aggregate expenditure:

Consumption function: C=20 + 0.8YD

Investment function: I = 30

Government expenditures: G = 8

Export function: X= 4

Import function: M=2 + 0.2Y

Tax rate, t = 0.2 or 20%.

Answer the following question.

1. What is the marginal propensity to consume in this economy?
2. What is the equation of the aggregate expenditure function in this economy?
3. Determine the size of the autonomous expenditure multiplier.
4. Determine the size of the tax multiplier.
5. What is the size of the budget deficit at the equilibrium level of income?
6. How much in tax cuts is required to increase the equilibrium level of income by 50.

Mr Brown is the manager of a portfolio consisting of stocks as shown below. the market risk premium is 8% and the risk free-rate is 3%

i) Calculate the beta and expected return of the portfolio

ii) Appraise & discuss why Mr Brown included stock Z in the portfolio

iii) Mr Brown strongly believe that the stock market would rise in the next one year. Discuss one possible way that he could use to increase the performance of the portfolio if the stock market were to rise.

1. The dependent variable has a score in the case of logistic regression. TRUE or FALSE and why?

2, If the probability of an even A is 0.2 and that of an event B is 0.10 then the odds ratio is: a.1 b. 2.25 c. 2.0 d. 0.5

3. In the case of logistic regression, we estimate how much the natural logarithm of the odds for Y =1 changes for a unit change in X. TRUE or FALSE

4. In binomial logistic regression, the dependent variables consists of more than two categories. TRUE or FALSE and why?

5. Similar to linear regression, logistic regression has one or more independent variables. TRUE or FALSE and why?