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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.