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- 14. In a regression context, under what situation is the predicted value for Y equal to the mean of Y? a) when the correlation between Y and X is positive b) when the correlation between Y and X is negative c) when the correlation between Y and X is zero d) when we try to predict Y in the complete absence of X e) a and d f) c and d g) none of the above, the predicted value for Y is only equal to the mean when X is equal to 032In a random sample of sixteen different industries the percentage employment x in STEM (science, technology, engineering, mathematics) and mean annual compensation y(in thousands of dollars) were recorded, with the following results. The scatter diagram showed a linear trend. SSxx = 1303.9 SSy= 1503.0 SSy = 2660.2 Ex = 150 .1 Ey = 915 n= 16 %3D %3D 1sxs 34 36.7 s y s 90.5 Calculate the linear correlation coefficient for percent employment in STEM and annual compensation and enter your answer below accurate to two decimal places.
- For each of the following, indicate whether the expected relationship between the two variables will be positive, negative, or zero. 1. The average number of calories eaten per day and body weight. 2. Air temperature and the amount of snow on the ground. 3. The number of minutes of exercise per day and score on a physical fitness test. 4. Number of absences and GPA. 5. Price of goods and height of a person.Please let me know if I calculated relative risk correctly. Thank you for your assistance.17. A risk manager would like to simulate the price of a stock using the discretized GBM, where St+At = St + µS{At+√ã$£€ where μ and o denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.5% and the weekly volatility is 4%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of μ? (a) = 26.4% (b) û = 30.16% (c) û = 4.5% (d) û = 17.94% 18. Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift μ = 0.01 and an annual volatility of o= 0.25. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GBM, the future price at T, i.e. ST, given today's spot price, St, is with TT-t and €~ = (a) 21.51% (b) 35.48% (c) 51.1% (d) 30.47% ST= St x exp (μ x exp [(μ-27 ) XT + √F X 0 Xe] N (0, 1).
- Suppose that x and y are unknowns with ?(?)=E(X)= 11, var(?)=Var(X)=4, ?(?)=E(Y)= 7 and var(?)=Var(Y)= 100. In addition, suppose that the correlation coefficient of ?Xwith ?Yis .6. Then what is the expected value of xy?1.The policy holder's loss function, X follows a distribution, ,X = 1 8 P(x) = x 2. x= 3 8. Find(i) the moment generating function (ii) Mean of X using moment generating functionIn a random sample of sixteen different industries the percentage employment x in STEM (science, technology, engineering, mathematics) and mean annual compensation y(in thousands of dollars) were recorded, with the following results. The scatter diagram showed a linear trend. SSx = 1303.9 SSsy= 1503.0 SSy = 2660.2 Ey = 915 n= 16 %3D Ex = 150 .1 1sx<34 36.7 s y < 90.5 Predict the mean annual compensation in industries in which 30 percent of the workforce are in a Stem field. You answer should be entered in thousands of dollars. Example: If you calculate y-hat as 40.6 then the answer you enter should be 40,600
- 3(ii) A bank sets up a Special Purpose Vehicle (SPV) for a CDO issue. The SPV wants to understand the risks that they may face, so they run simulations of the annual cash flows out of their portfolio. Selected results of the simulation are shown in the table below. Annual Portfolio Cash Flows Mean Std. Dev. Min. 5th 10th Percentiles 15th 85th 90th (1,172) 16,651 (7,760) (6,800) (4,880) (3,920) 2,480 95th Max. 14,320 15,280 26,400 The SPV wants to hold risk capital to cover its losses to the 95th percentile, and expected CDO payouts for the next five years add up to $100m. How much capital would you advise them to hold, and why?3. Suppose that X has an exponential distribution with a mean of 10. Determine the following: (a) P(X 15) (c) Compare the results in parts (a) and (b) and comment on the role of memoryless property.Let X₁,... Xn be sampled from a uniform distribution with support 0≤x≤0. a. Find the PDF of the second ordered statistic X(2) b. Find the expected value of X(2). You may use wolfram, but you must correctly write down what you are asking Wolfram to calculate for you. c. Find an unbiased estimator of 0, that is a function of X(2).