Download 1. (a) Define the term, random variable. (b) Identify the experiment in

REDEEMER’S UNIVERSITY
km 46/48 Lagos –Ibadan Expressway, Redemption City, Ogun State
COLLEGE OF MANAGEMENT SCIENCES
DEPARTMENT OF
ECONOMICS AND BUSINESS STUDIES
COURSE CODE /TITLE
ECO 106/Introduction to Statistics II
Second
SEMESTER EXAMINATIONS
2013/2014
SESSION
INSTRUCTIONS ON CHOICE OF QUESTIONS TO BE ANSWERED
Answer question one and any other two questions
TIME ALLOWED
1. (a)
(b)
(c)
(d)
2 hours
Define the term, random variable.
Identify the experiment in the act of tossing a fair coin three times.
Determine the sample space in question (1b) above.
In question (1b) above, a researcher is interested in the appearance of tail when a fair coin
is tossed three times. What is the random variable in this action?
From question (1d) above, represent the random variable with letter Y and determine the
probability distribution.
Compute the expected value of the probability distribution.
(30 marks)
(e)
(f)
2. (a) Interpret the following set formulations.
i)
ii)
iii)
iv)
v)
x A
A B
A B
A B
A
(b) Giving that A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}and B = (all even numbers in A}
Determine the following:
i) A  B
ii) A  B
(a) What is a normal distribution?
(i)
State two features a normal distribution must possess
(20 marks)
3. (a)
In a survey conducted by a researcher on policies to improve the living conditions among
students of the Redeemer’s University. It was discovered that 60% of the students supported
reduction in school fees; 50% supported provision of free meal while 30% supported both policies.
What is the probability that a student will support either of both policies?
(b). In an experiment involving tossing of a coin, the probability of head is given as ‘p’ while the
probability of a tail is ‘q’. Using a tree diagram what is the probability of tossing a fair coin twice?
(20 marks)
4. Monthly sales of a certain product, recorded to the nearest thousand, are believed to follow a
discrete probability distribution given in the table below. Supposed that the company has a fixed
monthly production cost of $8,000 and that each item brings $2. Find the expected monthly
profit from sales of the product and determine the variance.
(20 marks)
5. (a) Briefly differentiate between a Binomial and Poisson distributions?
(b) In the production of ballot papers for gubernatorial election in Ekiti State of Nigeria, it was
found that there were 3 defective printings out of every 15 papers. If five papers were picked at
random, find the probability that:
i) 2 are defective
ii) At most 2 are defective
iii) At least 2 are defective
iv) Determine the expected value and variance of this distribution.
Hint: Binomial distribution is required here.
(20 marks)