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Consider the linear model with n observations y ~ N (Xβ, σ2In), since we have many predictors, β is a vector.
(a) Write down the log-likelihood (β; y) of the model and the score U(β) = ∂/∂ β.
(b) Under certain regularity conditions it can be shown that the expected score is zero and thus that Fisher information I(β), the variance of the score, isShow that I(β)1 is the same as the variance of the MLE β of β, and thus that the information does not depend on β.
(c) The same regularity conditions imply that That is, that the information is also the negative Hessian of the log-likelihood. Verify that this is true by computing the negative Hessain and showing it equals the inverse of the variance of β.
An investor purchases a 30-year municipal bond for $940. The bonds coupon rate is 9 percent and, it still had eighteen years remaining until maturity. If the investor holds the bond until it matures and collects the $1000 par value and his marginal t..
On each no delinquent sale Cast Iron receives revenues with a present value of $1,360 and incurs costs with a present value of $1,210. Assume there is no possibility of repeat orders and that the probability of successful collection from the customer..
How much must you deposit at the end of each year for 15 years, to be able to withdraw $500 at the end of year 10 and $1000 at the end of year 15 if your savings earn interest at an annual rate of 7%?
General Mills has a $1,000 par value, 12-year bond outstanding with an annual coupon rate of 3.60 percent per year, paid semi-annually. Market interest rates on similar bonds are 12.70 percent. Calculate the bond's price today.
Michael Harper has $3,000 to invest for three years. He wants to receive $5,000 at the end of the three years. What invest rate would his investment have to earn to achieve his goal?
The debt has a one-year maturity and a promised interest payment of 11%. Thus, the promised payment to Backwoods’s creditors is $1,132.2. The market value of the assets is $1,220 and the standard deviation of asset value is 47% per year. The risk-fre..
Erna Corp. has 7 million shares of common stock outstanding. The current share price is $86, and the book value per share is $5. Erna Corp. also has two bond issues outstanding. The first bond issue has a face value of $70 million, has a coupon rate ..
Based on what I have read in this week’s chapter I would have to say Net Present Value is something we use at my job. My company decided to analyze the predicted profitability of one of its projects. In order to do so it had an initial cost of $10,00..
An investment has an installed cost of $535,800. The cash flows over the four-year life of the investment are projected to be $213,850, $230,450, $197,110, and $145,820. If the discount rate is infinite, what is the NPV?
A quasi-subjective project scoring approach to capital budgeting decisions:
Which of the following financial ratios/percentages would be the most likely reason for a bank to NOT approve a company’s application for a line of credit to fill temporary cash shortfalls?
Suppose you have a semi-annual coupon paying bond that has 10 years of maturity left, has a par value of $65,100, has a coupon rate of 7.23%, and has just paid its most recent coupon payment 10 days ago. What is this bond's annual yield based on a Ti..
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