Instructions: 1. The first test will be based on the following two questions. During the test, you have to compile the codes that should you have already written, and produce results for the parameter sets that you will receive during the test. [The param- eters given in the questions below are only for the purpose of testing your codes. During the actual test, each student will receive a different set of parameters. Hence, it is important that you are able to run the codes on your own and do not depend on the person who assisted you with the coding.] 2. For the programming part, you can work in a group and use a programming language of your choice. Then you will have to run the codes and show the simulations to me in person when we have the test on Thursday next week the 6th of March. You will not receive any marks or may receive only partial marks if you are not able to explain your code or if the answers are far from what they are supposed to be. 3. I might ask more theoretical explanations if any particular step in the code is not clear from your code. If your explanation is not satisfactory, you might loose some marks. Q.1 Using the information presented on page 25-26 (Chapter 2) of the book that we are using, write a programme to calculate (x). Check your programme for positive as well as negative values of x. Test your programme for x = 1.4 and x = -1.4. Furthermore, check that for any real value of x, (x) + (−x) = 1, e.g., (1.4)+(−1.4) = 1, $(3.2) + (-3.2) = 1, etc. Q.2 Starting at some fixed time, let F(n) denotes the price of a First Local Bank share at the end of n additional weeks, n ≥1; and let the evolution of these prices assumes that the price ratios F(n)/F(n-1) for n > 1 are independent and identically distributed lognormal random variables. Assuming this model, with lognormal parameters μ and σ, write a programme to calculate the probability that the price of the share at the end of the M weeks is higher than it is today? Test your programme for μ = 0.0165, σ = 0.0730, M = 2.. [For the calculation of (.), you may wish to use the code that you have developed while answering Q.1 above.]