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FIT 1006 Assignment
You should complete all of the three questions below. The marks for each question are equally weighted. Question 1: You have two biased dice, each with the following probabilities set out in the table below. Please calculate the following, showing your working and using appropriate notation: (a) The chance of rolling a six. (b) The chance of both dice having the same value. (c) The mean value expected from rolling both dice and summing the results. Dice 1: x P(x) 1.000 0.500 2.000 0.050 3.000 0.100 4.000 0.200 5.000 0.200 6.000 0.300 Dice 2: x P(x) 0.000 0.300 2.000 0.200 4.000 0.150 6.000 0.250 10.000 0.100 Question 2: You are interested in exploring the relationship between exam results and research performance. For the following data: (a) Calculate the q and r correlations. (b) Illustrate using a plot the correlations obtained in (a). (c) Provide an explanation and interpretation of what this means in practice, including which correlation is most appropriate to use. Exam Results Research Performance 5.000 8.067 10.000 22.372 4.000 8.608 5.000 10.955 6.000 12.756 Exam Results Research Performance 7.000 13.497 11.000 20.934 8.000 18.244 10.000 18.380 11.000 25.070 14.000 31.591 12.000 27.750 15.000 30.075 10.000 21.204 12.000 28.800 6.000 11.702 Question 3: Using probability theory, please explain how the T-test works, in a way that can be accessible to a lay person. You may use illustrations to support your explanation.