Company Law Questions
Question 1
Esanda Finance v Peat Marwick (1997) 188 CLR 241 and Daniels v Anderson (1995) 16 ACSR 607 are important decisions regarding auditor's liability. Explain why.
Question 2
With reference to case law and the Corporations Act 2001(Cth) describe what is meant by the term 'insolvency' and identify the link between 'voluntary administration', 'deeds of company arrangements', and 'liquidation'.
Question 3
"The law recognizes a corporation as a distinct legal entity, having a separate existence and a corporate personality of its own, quite apart from the members who comprise it." Discuss this statement with reference to the main legal consequences both at general law and under the Corporations Act 2001 (Cth).
(a) Describe two potential advantages of regression trees over other statistical learning methods. (b) When growing a regression tree using CART, two types of splits are considered. Describe these splits and provide an example for each. (c) A regression tree has three types of nodes: the root node, internal nodes and terminal nodes. Describe each node and explain how predictions are made using a regression tree. (d) Large bushy regression trees tend to over-fit the training data. Briefly explain what is meant by over-fitting and under-fitting the training data using regression trees. (e) The predictive performance of a single regression tree can be substantially improved by aggregating many decision trees. i. Briefly explain the method of bagging regression trees. ii. Explain the difference between bagging and random forest. iii. Briefly explain two differences between boosted regression trees and random forest.2. In the carseats data set, we will seek to predict Sales using regression trees and related approaches, treating the response as a quantitative variable. 3) Split the data set into a training set and a test set. b) Fit a regression tree to the training set. Plot the tree, and interpret the results. What test MSE. RMSE and MAPE do you obtain? Compare them to training errors. c) Determine the optimal level of tree complexity. Try to prune the tree and explain whether pruning the tree improve the test MSE. 5. Consider the system 11 12 Co 13 (a) Create a Jacobi iterative formula that is guaranteed to converge for solving the above system of equations. (Hint: you need to rearrange the equations) (b) Compute 10 Jacobi iterations (use your calculator) starting with x(0) = 0. (c) Create a Gauss-Seidel iterative formula that is guaranteed to converge for solving the above system of equations. (d) Compute 10 Gauss-Seidel iterations (use your calculator) starting with x(0) = 0. (e) Compute the exact solution (any way you like). (f) Between the Jacobi and the Gauss-Seidel iterative methods, which one is faster? 6. Solve the linear system 2x1 - 22 + 23 = 2x1 + 2x2 + 213 = -X1 - 22 + 213 = iteratively. (a) Use the Jacobi method with x ) = 0 to compute the next 10 Jacobi iterations (use your calculator). (b) Compute the exact solution (any way you like) and use it to find the co-norm of the error in 5th Jacobi iterate. 32Question 2. Use Jacobi and Gauss Seidel iterations to find xk. start with Xo = [0 1 0 3], for the system. X1 + 3X3 2x2 +5X4 4x| +3x3 = 6x2 + 3x4 = a. How many iteration did Jacobi method obtained? b. How many iteration did Guass - Seidel method obtained? C. Which is the best method
