University of the Free State
Department of Mathematical Statistics and Actuarial Science
WKS216 TEST 1 Date: 25 February 2013 Time: 11/2 hours Total: 50
1. Define the following concepts:
a) Moment generating function
b) Convergence in probability.
(3)
(3)
Practical 9 Memo
By using the data in the table below, calculate for 2005 with 2002 as
base year: / Deur gebruik te maak van die data in die onderstaande
tabel bereken vir 2005 met 2002 as basis jaar:
2002
Product p0 q0
I
80 50
II
50 30
III
30 30
Total
A
1.
The average score of all pro golfers for a particular course has a mean of 70 and a
standard deviation of 3.0. Suppose 36 pro golfers played the course today. Find the
probability that the average score of the 36 pro golfers exceeded 71. / Die gemiddel
Practical 10
1.
A R1 000 is deposited into a bank account on 1 May and withdrawn on 31October of the
same year. Find the future value if the interest rate is 10% simple interest. / n R 1 000 is
gedeponeer in n bankrekening op 1 Mei en onttrek op 31 Oktobe
Practical 9
By using the data in the table below, calculate for 2005 with 2002 as base year: / Deur
gebruik te maak van die data in die onderstaande tabel bereken vir 2005 met 2002 as basis
jaar:
Product
I
II
2002
p0
q0
80
50
50
30
2005
P1
q1
70
70
40
60
PRACTICAL 5
1.
The table below gives the probability of combinations of religion and political parties in a
major South African city
Political Party
ANC
DA
COPE
Prostestant
0.35
0.27
0.05
Catholic
0.10
0.09
0.03
Muslim
0.03
0.02
0.02
Other
0.02
0.01
0.01
Practical 2
The marks obtained in the previous class test out of 20 were as follows:
20
10
10
10
13
16
1
2.
3.
4.
9
18
2
8
16
12
14
17
11
5
11
14
12
11
11
15
20
12
19
8
17
7
Define the random variable and the data type: Marks and Discrete
Find the range:
Practical 3 Memo
1.
n=9
2.
The range, R = 32 - 19 = 13
3.
The mean =
225
X =
=25
9
n+1
=5
2
4.
The order number of median
5.
The median = 25
6.
The mode, Mo = 25
7.
The lower quartile. Order number = 2.5;
The lower quartile = 22
8.
The third quartile. Ord
Practical 7 Memo
1.
A balanced coin is tossed 8 times. Let X denotes the number of heads. Calculate the
following: / n Gebalanseerde muntstuk word 8 keer gewerp. Laat X die aantal
munte aandui. Bereken die volgende:
1.1
P ( X=5 ) = 8 0.55 0.53=0.21875
5
1
EBCS 1514 Practical 1 Memo
1.
The following table represents the number of students registered for a specific course
at various universities.
University
Number of Students
A
880
B
540
C
720
D
460
A sample size of 260 students must be drawn from this popul
Practical 4
Question 1
Using the empirical rule, Mrs. G found that 95% of the population is aged between 14 and 42.
1.1
Calculate the mean and the standard deviation
1.2
Find the boundaries that will cover 99.7% of the population.
1.3
Find the boundaries
Practical 2
The marks obtained in the previous class test out of 20 were as follows:
20
10
10
10
13
16
1
2.
3.
4.
8
16
12
14
17
11
5
11
14
12
11
11
15
9
18
20
12
19
8
17
7
Define the random variable and the data type
Find the range
What is the number of c
Practical 4 Memo
Question 1
Using the empirical rule, Mrs. G found that 95% of the population is aged between 14 and
42.
1.1 Calculate the mean and the standard deviation
2 =14
+2 =42
2 =14
=14 +2
+2 =42
( 14+2 ) +2 =42
14+ 4 =42
4 =28
=7
=14+2
14+2
WKS216 TEST 1 MEMO
Date: 25 February 2013
Time: 11/2 hours
1.
a)
b)
2.
a)
b)
3.
MY(t) = E(etY) = E(eX ) = E(eX ) = E(eX ) (because of independence)
= MX (t)
i
i
i
i
4.
and and
which is the MGF of a gamma random variable with parameters .
so is a gamma ran
PUNTE
MARKS
' 2' %
(Skry bei Fame van die papier)
(Please ite on both sides of the paper)
Van: Voorletters:
IIII
Mnr/Mev/Mej H/
Surname: Initials: Mr/Mrs/Miss
Student Number: 61 7 3 S 6 7 Evening or day student: _____ .................
MAIN CAMPUS
WKS 226
UNIVERSITY OF THE FREE STATE
EXAMINATION: NOVEMBER 2007
ASSESSOR: Dr. I.Garisch
Mr. D. Chikobvu
MODERATOR: Mr. A.M. Naude
TIME: 3 Hours MARKS: 100
Question 1
A certain phenomenon is either present or not. An apparatus has a prob
Practical 10 Memo
1.
After some consideration it has been decided to change the base year for the fuel index
from 2000 to 2005.
1998
1999
2000
2001
2002
2003
2004
2005
2006
2.
(2005=100)
90
96
100
105
110
120
110
80
140
112.5
120
125
131.25
137.50
150
137
Practical 6
Question 1
Given/Gegee: Z ~ N(0, 1).
1.1
P(- 2.15 < Z < 1.52)
1.2
P(Z > 2.18)
1.3
P ( Z >1.5 )
1.4
P ( Z <0.68 )
1.5
P ( 0.2< Z <1.5 )
1.6
P (2.89<Z<1.05 )
1.7
P ( Z <3.2 )
Calculate/Bereken:
Question 2
A luxury passenger liner has 500 passeng
Practical 7
1.
2.
A balanced coin is tossed 8 times. Let X denotes the number of heads. Calculate the
following: / n Gebalanseerde muntstuk word 8 keer gewerp. Laat X die aantal
munte aandui. Bereken die volgende:
1.1
P(X = 5)
1.2
P(X
1.3
P(X > 2)
2)
Give
Practical 3
Question 1
Given:/ Gegee:
25
26
21
19
30
32
25
24
23
Find: / Bepaal:
1.
n
( the number of data points / aantal data punte)
2.
the range / die variasiewydte
3.
the mean / die gemiddelde
4.
the order number for the median / die posisie van die m
EBCS 1514
Practical 1
1.
The following table represents the number of students registered for a specific course
at various universities.
University
Number of Students
A
880
B
540
C
720
D
460
A sample size of 260 students must be drawn from this population