Hello, dear friend, you can consult us at any time if you have any questions, add  WeChat:  zz-x2580

STAT7055 Introductory Statistics for Business and Finance

Exam Conditions:
Central examination.
Students must return the examination paper at the end of the examination.
This examination paper is not available to the ANU Library archives.
Materials Permitted in the Exam Venue:
(No electronic aids are permitted, e.g., laptops, phones).
Calculator (non-programmable).
Two A4 pages with notes on both sides.
Unannotated paper-based dictionary (no approval required).
Materials to be Supplied to Students:
Script book.
Scribble paper.
Instructions to Students:
Please write your student number in the space provided on the front of the script book.
Attempt all 5 questions.
Start your solution to each question on a new page and clearly label each solution with the corresponding
question number.
To ensure full marks show all the steps in working out your solutions. Marks may be deducted for failure
to show working or formulae.
Selected statistical tables are attached to the back of the examination paper.
If a required degree of freedom is not listed in a statistical table, please use the closest degree of freedom.
Unless otherwise stated, use a significance level of α = 5%.
Round all numeric answers to 4 decimal places.
Question: 1 2 3 4 5 Total
Marks: 19 17 17 9 41 103
Question 1 [19 marks]
(a) [4 marks] A student answers a multiple-choice examination question that offers
four possible answers. Suppose that the probability that he knows the answer to
the question is 0.8 and the probability that he guesses is 0.2. Assume that if the
student guesses, the probability of selecting the correct answer is 0.25. If the student
correctly answers a question, find the probability that he really knew the correct
answer.
(b) [5 marks] Suppose the student takes an examination with 3 multiple choice ques-
tions. Let X denote the number of questions he gets correct. Assuming that the
student answers each question independently, determine the probability distribution
of X and calculate the expected value of X.
(c) [10 marks] Suppose the student takes an examination with 2 multiple choice ques-
tions. But this time, he gains confidence every time he knows the answer to a ques-
tion. Specifically, if he knows the answer to the current question, then for the next
question the probability that he knows the answer becomes 0.9 and the probability
that he guesses becomes 0.1. If he does not know the answer to the current ques-
tion, then for the next question the probability that he knows the answer and the
probability that he guesses remain 0.8 and 0.2, respectively. Again letting X denote
the number of questions he gets correct, determine the probability distribution of X
and calculate the expected value of X. We can assume the probabilities of knowing
the answer and guessing for the first question are 0.8 and 0.2, respectively.
Past Final Examination 1 Page 2 of 7 STAT7055