Year   Percentage
2000   28
2001   32
2002   36
2003   40
2004   44
2005   51
2006   53
2007   57
2008   60
2009   66

Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment.

alpha= 0.3 and beta= 0.4. Then calculate MAD.

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Quarter   Price
Q1 2017   186.3
Q2 2017   190.9
Q3 2017   195.2
Q4 2017   195.2
Q1 2018   198.7
Q2 2018   201.2

Forecast the price index for Q3 2018 using a​ three-period simple moving average. Then calculate MAD.

Two companies, ABC and XYZ, are considering entering into a swap. Company ABC can
borrow at a fixed rate of 8.1% or, alternatively LIBOP + 1.3%. Company XYZ faces a fixed rate of
7.5% and a floating rate of LIBOR + 0.3%.
a) Suppose that company ABC wants a floating rate loan, while company XYZ wants a
fixed rate loan. Is there a basis for a swap? If so, set up the swap under the assumption
that interest rate savings is split evenly by the firms.
b) Answer the same question under the assumption that company XYZ wants a floating
rate loan, while company ABC wants a fixed rate loan.

A portfolio of $ 100,000 is composed of two assets: A stock whose expected annual return is 10% with an annual standard deviation of 20%; A bond whose expected annual return is 5% with an annual standard deviation of 12%. The coefficient of correlation between their returns is 0.3. An investor puts 60% in the stock and 40% in bonds.

What is the expected annual return, standard deviation of the portfolio

What is the 1-year 95% VaR? Explain in non-technical terms the meaning of the number you calculated.

What is the 1-year 99% VaR? Explain in non-technical terms the meaning of the number you calculated

Discuss the weaknesses of Value-at-Risk as a measure of risk.

A laser beam of intensity I irradiates at normal incidence a face of area A of a cubical sample of intrinsic silicon of volume V. The photons from the laser beam are absorbed uniformly throughout the Si sample.

(i) If the quantum efficiency of intrinsic Si is ?, determine an expression for the electron-hole pair generation rate in the Si sample.   

(ii) Determine an expression for the excess carrier concentration, ??, under steady state conditions.

(iii) Calculate the ratio of the conductivity under illumination, ?light, to the conductivity without illumination, ?dark, for a Si sample of V =1 cm3,

A = 1 cm2, I = 1 mW cm-2, ? = 632.8 nm and ? = 0.3.

Stock Xillow has an expected return of 16% and a standard deviation of 4%. Stock Yash has an expected return of 12% and a standard deviation of 3%. Assume you have constructed a portfolio consisting of 75% weight in Stock Xillow and 25% in Stock Yash. Furthermore assume that the stocks have a correlation coefficient of -0.3. What is the standard deviation of the portfolio? A. Less than 2% B. Greater than or equal to 2% and less than 2.5% C. Greater than or equal to 2.5% and less than 3% D. Greater than or equal to 3% and less than 3.5% E. Greater than or equal to 3.5%

An experiment has 5 treatments; 6 replicates were obtained for each of the treatments. Use the treatments below to solve

A) Do the ANOVA computations on this data; what is the P-value?

B) On the basis of this P-value, do you reject the hypothesis that the means of the 5 treatments are the same at an α = 0.05confidence level?

A battery pack used in a medical device needs to be recharged about every 5 hours. A random sample of 20 battery packs is selected and subjected to a life test. The average life of these batteries is 5.05 hours with standard deviation ?=0.3 hours. Assume that battery life is normally distributed. Is there evidence to support the claim that mean battery life is more than 5 hours? Use ?=0.01.

a. Use P-value approach to test the hypothesis.
b. Use t-test to test the hypothesis.
c. Use confidence interval to test the hypothesis

d. If the true mean life is 5.1 hours, what is the type II error?

The following table shows the quarterly demand in thousands of cases, for a national beer distributor over the past four years. This data is also available in an Excel spreadsheet on Blackboard.

1.                                                                                         Using a smoothing coefficient of a = 0.3, exponentially smooth the series. Assume an initial forecast for the first quarter of 2015 of 300. Show:

- the MAD and MAPE

- a plot of the actuals and forecast on a properly labeled chart.

- the forecast for the first quarter of 2019.

• What is the conservative critical F statistic if your sample size is 50 and you are comparing 3 groups of participants (at the .05 level)?
• What is the critical F statistic value for the following F (4,70), use a .05 level of significance?
• If you have an MS between of 3.1 and MS within groups of 0.3, what would your calculated F statistic be?
• If you saw the result of ANOVA like this F(2,40) = 4.5, how many groups were in the study and how many participants were in the study?

Give an example of when you would use a one-way ANOVA. What is dependent and what is independent variable?

Question
(a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257.
Calculate the unbiased estimator of the population variance.
(1 mark)

(b) Suppose the GPA of all students enrolled in a particular course can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Compute the probability that the
mean GPA of a random sample of 40 students selected from this course will be:

(i) lower than 3.2

(ii) between 3.3 and 3.6

(c) Suppose you throw a die 600 times. Apply a suitable technique to compute the
approximate probability of obtaining between 90 and 110 fours.