| University | The Open University (OU) |
|---|---|
| Subject | B126 Business Data Analytics and Decision Making |
B126 TMA02 Questions
TMA02 has five questions. Your answers are each question. Before doing so, ensure that you have read the materials and guidance notes related to each question. Before doing so, ensure that you have read
Part 1 (20 marks)
Game rules
- If you put a 1 or 2, you lose £10.
- If you put a 3, 4 or 5, you win £10.
- If you put a 6, you win £20.
Let x be the random variable representing your possible winnings from one roll of the die.
Answer the following questions.
a. Using the definition of a discrete random variable, construct the probability distribution of x. (2 marks)
b. Derive the expected value E[X] of possible winnings and discuss its meaning in the context of this game. (2 marks)
c. Compute the variance Var(X) and explain what it measures. (2 marks)
d. Calculate the standard deviation σ(X) and the range of X. (2 marks)
e. Use the results you got in points a) to d) to discuss the risk and reward for a player in this game. (8 marks)
f. Explain the four characteristics of the normal distribution. (4 marks)
Note: Your answer should show all intermediate steps clearly, use proper notation and include a brief explanation of each result in words. For calculations, you need to show the detailed workings.
The suggested length of answer to Part 1 is about 300 words.
Guidance notes for Part 1
Review Unit 2, Session 2 to understand the probability distribution, expected value, variance and standard deviation. You are expected to know how to calculate these figures and comment on these figures. Also, refer to Section 4 of Session 2, Unit 2 to understand the normal distribution.
Part 2 (20 marks)
Part A (normal distribution, t-distribution and F-distribution)
Alex, a tutor, collects the marks from TMA 02. These marks follow a normal distribution, with an average of 55 and a standard deviation of 14.
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