<p> EWU – ECON 437 – Econometrics – Briand</p><p>Homework assignment #1 (20 points)</p><p>General Rules for Homework Assignments (apply to all assignments):</p><p> Try to do the problems first on your own.  Then meet with other students to discuss problems.  Talk to Becky or other TA who have taken Econ 437 before.  If you still have problems, see me.  Be organized. Give me a report on your results in the order of the problems. Either written by hand or with a word processor. If computer work with Excel is required for a problem, print a copy of the excel worksheet with the results and attached it to the report, or copy the excel worksheet with the results and paste it in the report.  Create a new excel file for every homework assignment and create a new worksheet in your file for every problem that requires computer work.  I prefer that you e-mail the computer part of your homework to me ([email protected]). However, you can bring a CD or thumbnail to me if you have e-mail problems. NOTE: write the name of your excel file as the subject of the email.  Excel files be should be named as followed: econ437hmk#LastName.xls. Each worksheet within the excel file should be named as followed: Q#. </p><p>NOTE: 1 point for following above instructions</p><p>1. Express the following sums in summation notation: a) x1 + x2 + x3 + x4 (0.5 point) b) x3 + x4 (0.5 point) c) x11 + x12 + x21 + x22 (0.5 point) d) x1 – y1 + x2 – y2 + x3 – y3 (0.5 point)</p><p>2. Let X be a discrete random variable that is the value shown on the single roll of a fair die. a) Represent the probability density function f(x) in tabular form (1 point) b) What is the expected value of X? (1 point) c) Find the expected value of X2. (1 point) d) Find var(X). (1 point)</p><p> show your calculations! EWU – ECON 437 – Econometrics – Briand</p><p>3. The joint probability density function of two discrete random variables X and Y is given by the following table: Y 1 3 9 2 1/8 1/24 1/12 X 4 1/4 1/4 0 6 1/8 1/24 1/12</p><p>Find the covariance of X and Y (5 points)</p><p> show your calculations!</p><p>4. Based on long years of experience, an instructor has determined that in her principles of economics class the probability distribution of X, the number of students absent on Mondays, is as follows:</p><p> x 0 1 2 3 4 5 6 7 f(x) 0.005 0.025 0.310 0.340 0.220 0.080 0.019 0.001</p><p> a) Find the probability that a given Monday either two or three or four students will be absent (1 point) b) Find the probability that on a given Monday more than three students are absent (1 point) c) Compute the expected value of the random variable X. Interpret this expected value. (1 point) d) Compute the variance of the random variable X (1 point) e) Compute the expected value of Y = 7X + 3 (2 points) f) Compute the variance of Y= 7X + 3 (2 points)</p><p> show your calculations!</p>