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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: 2008/2009
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 1301: PROBABILITY AND STATISTICS
DATE: AUGUST 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) Sample space
ii) Frequency distribution
iii) Arithmetic mean
iv) Kurtosis
v) Correlation
vi) Mutually exclusive event
(6 Marks)
b) Let A and B be two events in a random experiment with P(A) = 0.38 and
P(B) = 0.25. Find the probability that either A or B occurs if:
i) A and B are mutually exclusive events
ii) A and B are independent events
(4 Marks)
c) i) Using a clearly labeled diagram, show the position of the mean, mode and median of a
positively skewed distribution. (2 Marks)
2
ii) Given the data set 33, 35, 37, 37, 39, 39, 41, 41, 41, 42, 44, calculate the mean, median
and standard deviation. Hence calculate the Karl Pearson’s coefficient of skewness.
Comment on the distribution of the data. (7 Marks)
d) 100 students pursuing a course in IT were examined and their results were summarized as
shown in the table below:
Marks Number of students
20 – 24
25 – 39
40 – 49
50 – 54
55 – 69
70 – 79
a
20
b
15
20
10
Given that the median mark is 47.5. Determine the values of a and b. (5 Marks)
e) In a large batch of items, 5% are defective. If 50 items are selected at random from the batch,
what is the probability that:
i) At least one will be defective
ii) Exactly two will be defective (6 Marks)
QUESTION TWO
a) Two discs are drawn without replacement from a box containing three red and four white discs.
If x is the random variable “the number of white discs drawn”, find:
i) E[x] (6 Marks)
ii) E ??x2?? (2 Marks)
iii) Var x (2 Marks)
iv) Var (3x - 4) (2 Marks)
3
b) Given the moment generating function ( ) 3t 8t2
x M t =e + , find the moment generating function of
the random variable 1( 3)
4
Z= x- , and use it to determine the mean, and the variance of Z.
(8 Marks)
QUESTION THREE
a) The following data was obtained from the sales records of LYRU, a second hand motor vehicle
dealer.
Age of motor
vehicles
7 9 8 14 9 7 9 10 5 8
Selling price
Shs. ‘000’
700 495 450 380 485 720 560 450 1250 650
Using ordinary least squares equation, estimate the selling price of a six year old
motor vehicle. (10 Marks)
b) i) Differentiate between a discrete and a continuous random variable. (2 Marks)
ii) If X is a discrete random variable with probability distribution function f (y)defined by
6
y , for 1, 2, 3. Find the mean and standard deviation of Y. (4 Marks)
iii) If a random variable X has the pdf ( )
3 0
0
Ke x for x
f x
elsewhere
? - >
=??
Find K and P(0.5 =x=1) (4 Marks)
QUESTION FOUR
The masses in grams of 50 small fruits are shown in the following table,
Mass grams Number of Fruits
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
100 – 109
110 – 119
4
5
9
14
7
6
5
4
a) Draw a histogram to represent the data. (3 Marks)
Calculate the:
b) Mean (3 Marks)
c) Mode (3 Marks)
d) Median (3 Marks)
e) Standard deviation (4 Marks)
f) Interquartile range of the distribution. (4 Marks)
QUESTION FIVE
a) A set of computer science students sat probability and statistics and programming papers in the
April 2009 examination. The marks obtained by the candidates were as follows.
Probability
and statistics
%
8 12 21 34 36 42 43 53 54 58 70 83
Programming
%
20 15 18 22 41 42 50 43 54 62 70 85
i) Draw a scatter diagram to show the above scenario. (2 Marks)
ii) Determine the rank correlation coefficient and comment on its value. (8 Marks)
b) A student is likely to wake up on time with a probability ¾ . If he wakes up on time, there is a
probability of 9/10 that he will arrive in the dining hall in time for breakfast. If he oversleeps, there
is a probability of ½ that he will arrive at the dining hall in time for breakfast. If he is late in
arriving at the dining hall, there is a probability of 2/3 that he will miss breakfast, but on any
occasion he arrives at the dining hall on time, he has breakfast.
i) What is the probability that on any one day, he will miss breakfast? (3 Marks)
ii) If he misses breakfast, what is the probability that he woke up late? (4 Marks)
iii) If the student arrives late for breakfast one day, what is the probability that he woke up late?
(3 Marks)
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