Question. Help in solving the questions below. Kindly address all the questions. Thanks in advance.

1.Assume that a country's production function is Y = AK 0.3 L 0.7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product.

a.What is the marginal product of capital in this situation?

b.If the economy is in a steady state, what must be the saving rate?

c.What is the marginal product of capital if the economy reaches the Golden Rule level of capital?

d.What must the saving rate be to achieve the Golden Rule level of capital?

Sales person for widgets make a sale to 15% of the customers on whom they call. If a member of the sales calls on 15 customers today, what is the probability that he/she will sell, i. exactly two widgets ii. at most two widgets 111. at least three widgetsAn actuary is fitting the following linear regression model through the origin: Y =Bx;te, e; ~ N(0,0-) i=1,2. . ..n (i) Show that the least squares estimator of / is given by: B (ii) Derive the bias and mean square error of S under this model.A company examining its employee retention rates considers the number of complete years a new employee works for a particular division before leaving. The results are shown in the table below: Division A 6 Division B Do UP + Division C 10 5 7 (i) Perform a one-way analysis of variance at the 5% level to compare the retention rates for the three divisions. [5] (ii) Present the data in a simple diagram and hence comment briefly on the validity of the assumptions required for the analysis of variance. [2] (iii) Concern is expressed over the variability of the results in Division B. It is thought that this might be significantly different from the assumed common underlying variance. (a) Write down an estimate for the underlying common variance for all three divisions. (b) Calculate an unbiased estimate for the variance in Division B based on the data for Division B only. (c) Test at the 5% level whether the variance in Division B is significantly different from your estimate in (iii)(a). [5] [Total 12]