Get premium membership and access revision papers, questions with answers as well as video lessons.
Probability And Statistics Question Paper
Probability And Statistics
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2009
UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 1301: PROBABILITY AND STATISTICS
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Briefly define the following terms as used in probability and statistics.
i) Statistics
ii) Mathematical expectation
iii) Probability distribution function
iv) Skewness
v) Correlation
vi) Mutually exclusive events (6 Marks)
b) Given that two events X and Y are independent, copy and complete the contingency table below.
Y Y
X 3
20 1
2
X
1
4
2
i) Find P(XUY) (3 Marks)
ii) P(X Y) (3 Marks)
c) A distribution consists of three components with frequencies 45, 60 and 65 having their means as
2, 2.5 and 2 respectively, and standard deviation 0.1, 0.5,0.8 respectively. Calculate:
i) The mean (2 Marks)
ii) The standard deviation
Of the combined distribution (3 Marks)
d) 60 students pursuing a course in IT were examined and their results summarized as shown in the
table below.
Marks f
25 – 29
30 – 34
35 – 39
40 – 44
45 – 49
5
12
25
11
7
Calculate:
i) Mean mark (3 Marks)
ii) Mode (3 Marks)
iii) Median (3 Marks)
iv) Standard deviation (4 Marks)
QUESTION TWO
a) The table below gives a probability of a discrete random variable X.
X 4 8 12 15 20
P(X = x) v 0.25 0.3 w 0.1
Given thatP(x<13)=0.75,
Find
i) value of v and w (3 Marks)
ii) E(x) (2 Marks)
iii) P(x>9) (2 Marks)
3
iv) Var X (4 Marks)
v) Var (3x - 4) (2 Marks)
b) i) Find the moment generating function of a Poisson distribution with a probability distribution
function
( ) 0,1, 2,
!
f x xe for x
x
?? -?
= = ??
(5 Marks)
ii) Hence find the mean of X. (2 Marks)
QUESTION THREE
a) The mileage Y that can be covered with a litre of a certain brand of gasoline depends on the
amounts X of a certain chemical additive in the gasoline. The following were results from 10
pairs of observations X and Y.
83.16 i i S x y =
2 3.85 i S x =
5.5 i S x =
( )2 41.041 i S y -y =
2 2048.93 i S y =
b) Determine the product moment correlation coefficient and coefficient of determination between X
and Y comment. (10 Marks)
c) Use the method of least squares to fit a regression line that can be used to predict mileage Y given
the amount of chemical additive X in the gasoline. (8 Marks)
d) Estimate the mileage Y given that the amount of additive is 0.35. (2 Marks)
QUESTION FOUR
a) Members of a consulting firm rent cars from three rental agents. 60% of the cars are from agency
A, 30% from agency B and 10% from agency C. 9% of the cars from agency A needs a tune up,
20% from agency B need a tune up and 6% from agency C need a tune up.
i) What is the probability that a rental car delivered to the consulting firm will need a tune
up? (5 Marks)
4
ii) If a rental car delivered to the consulting firm needs a tune up, what is the probability that
it came from agency B? (5 Marks)
b) The table below shows the weights in Kg of 100 male students in KCA university.
Weight f
60 – 62
63 – 65
66 – 68
69 – 71
72 – 74
5
18
42
27
8
i) Draw a histogram to represent the data. (3 Marks)
Calculate
ii) Mean (3 Marks)
iii) The interquartile range of the distribution (4 Marks)
QUESTION FIVE
a) The first 4 moments about X = 10 for a particular distribution are 4, 80, 320 and 800.
Determine:
i) The mean (3 Marks)
ii) The variance (3 Marks)
iii) The 3rd and 4th moments about the mean (6 Marks)
b) Using a clearly labeled diagram, show the position of the Mean, mode and median of a negatively
skewed distribution (3 Marks)
c) In a certain statistical distribution, the following results were obtained: X = 45, Median = 48,
coefficient of skewness = -0.4. Calculate:
i) Mode (2 Marks)
ii) Standard deviation (3 Marks)
More Question Papers
Popular Exams
Return to Question Papers