Institute of Actuaries of India
Subject CT3 Probability & Mathematical Statistics
May 2012 Examinations
Indicative Solutions
The indicative solution has been written by the Examiners with the aim of helping candidates. The
solutions given are only indicat

Subject CT3 Probability & Mathematical Statistics
November 2011 Examinations
INDICATIVE SOLUTIONS
IAI
Q1
CT3 1111
The probability distribution is
X :
:
0
p
E(X) =
E(
1
1-2p
2
p
= 0 * p + 1 * (1-2p) + 2 * p = 1
)=
=
Var(X) = E(
*p+
* (1-2p) +
* p = 1 + 2p

f
INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
21st May 2012
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (15.00 18.00)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1.
Please read the instructions on the front page of ans

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
20th May 2013
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (10.00 13.00)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1. Please read the instructions on the front page of answe

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
8th November 2010
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (15.00 18.00 Hrs)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1.
Please read the instructions on the front page

Institute of Actuaries of India
Subject CT3 Probability & Mathematical Statistics
May 2013 Examinations
Indicative Solutions
The indicative solution has been written by the Examiners with the aim of helping candidates. The
solutions given are only indicat

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
20th May 2014
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (10.30 13.30 Hrs.)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1. Please read the instructions on the front page of

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
11th November 2013
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (10.30 13.30 Hrs.)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1. Please read the instructions on the front pag

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
08th November 2011
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (15.00 18.00)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1.
Please read the instructions on the front page of

INSTITUTE OF ACTUARIES OF INDIA
EXAMINATIONS
19th November 2012
Subject CT3 Probability & Mathematical Statistics
Time allowed: Three Hours (15.00 18.00)
Total Marks: 100
INSTRUCTIONS TO THE CANDIDATES
1. Please read the instructions on the front page of

Institute of Actuaries of India
Subject CT3 Probability & Mathematical Statistics
November 2012 Examinations
Indicative Solutions
The indicative solution has been written by the Examiners with the aim of helping candidates. The
solutions given are only in

Institute of Actuaries of India
Subject CT3 Probability & Mathematical Statistics
May 2012 Examinations
Indicative Solutions
The indicative solution has been written by the Examiners with the aim of helping candidates. The
solutions given are only indicat

iDUf clienl IS 3 IT'IEIHEIBCIUHDQ companv WDHE BEBE! "E numEr DI HEIECIWE pails
produced bv its production lines at its Nebraska plant. You design a one—tailed test to
prove that the dollar value of defects id} per dayr is less than $5,000. You establish

Actuarial Society of India
EXAMINATIONS
June 2005
CT3 probability and Mathematical Statistics
Indicative Solution
Q.1
a)
i)
ii)
b)
Stem and leaf display of the given data
4
8
5
0
1
7
6
1
3
6
6
7
7
1
2
2
3
6
8 8
8
2
4
4
5
7
9
9
3
4
9
10
0
Range = 100 48 =

Institute of Actuaries of India
Subject CT3-Probability and Mathematical Statistics
May 2008 Examination
INDICATIVE SOLUTION
Introduction
The indicative solution has been written by the Examiners with the aim of helping candidates.
The solutions given are

Subject CT3 Probability & Mathematical Statistics
November 2011 Examinations
INDICATIVE SOLUTIONS
IAI
Q1
CT3 1111
The probability distribution is
X :
:
0
p
E(X) =
E(
1
1-2p
2
p
= 0 * p + 1 * (1-2p) + 2 * p = 1
)=
=
Var(X) = E(
*p+
* (1-2p) +
* p = 1 + 2p

Institute of Actuaries of India
Subject CT3-Probability and Mathematical Statistics
October/Nov 2007 Examination
INDICATIVE SOLUTION
IAI
CT3 1007
1. The mgf of Bernoulli distribution is
MX(t) = E[etX]
= e tx p x q 1 x ; 0<p<1
x = 0 ,1
= (q+pet)
Hence, M X

Institute of Actuaries of India
Subject CT3 Probability & Mathematical
Statistics
May 2010 Examinations
INDICATIVE SOLUTIONS
Introduction
The indicative solution has been written by the Examiners with the aim of helping candidates. The
solutions given are

Institute of Actuaries of India
CT3: Probability and Mathematical Statistics
October2009Examination
IndicativeSolutions
IAICT31009
Q.1)
For280observations(whichincludetheincorrectvaluesof64and80),samplemean=54and
samples.d.=3.
Incorrectsamplemean=
where

Actuarial Society of India
Examinations
November 2005
CT3 Probability and Mathematical Statistics
Indicative Solutions
CT3
Q.1)
Nov 05
Median = 176
Q1 = 4.25th item = 136.5
Q 3 = 11.75th item = 245
Alternativ ely
Q1 = 136 and Q 3 = 253
[1]
50
Q.2)
100
150

Institute of Actuaries of India
Subject CT3 Probability and Mathematical Statistics
November 2010 Examinations
INDICATIVE SOLUTIONS
Page 1 of 12
IAI
Sol. 1)
CT3 November 2010
(a) sample mean = 3125
sample standard deviation = 1316.64
(b) for k = 2
upper b

Institute of Actuaries of India
CT3: Probability and Mathematical Statistics
May 2009 Examination
Indicative Solutions
IAI
1. a)
CT3 05099
12 14 19 20 21 28 29 30
32.8(mean)
55
63
_._._._._._._._._._._ 63._
28 (median)
b) Median 28
Mean 32.18
Locations in

Institute of Actuaries of India
CT3: Probability and Mathematical
Statistics
Indicative Solution
November 2008
Introduction
The indicative solution has been written by the Examiners with the aim of helping candidates.
The solutions given are only indicati

Actuarial Society of India
Examinations
November 2006 Examinations
CT3 Probability and Mathematical Statistics
Indicative Solutions
CT3
1006
1. i) Minimum : 47
Maximum : 60
Q1 : 11th smallest 50
Q2 : Average of 21 st and 22nd smallest
Q3 : 32nd smallest 5

The Institute of Actuaries of India
Subject CT3 Probability & Mathematical
Statistics
15th May 2007
INDICATIVE SOLUTION
Introduction
The indicative solution has been written by the Examiners with the aim of helping
candidates. The solutions given are only

A standard normal distribution is
a} a generic name for any.r probability.r distribution.
' b} a particular normal distribution, with a mean of zero and a standard deviation of
one.
c} the same as a normal distribution.
d} a distribution where the mean is

You are testing vehicles of the same brand and model to determine their gas mileage.
After testing 100 vehicles, vou have calculated the sample mean is} to be 25 mpg and
the sample standard deviation is} to be 2.1 mpg. To have a better idea of the accurac

Expected oomte are below observed comte
Accident No Accident Total
l-leallryr 11 B 1?
3. TB 3.24
Moderate 9 9 13
9.2? 3. ?3
Nonamoker 14 1? 31
1 5.9? 1 5.03
Total 34 32 BB
Ci‘i- = 1.?0, DF = 2, P-Value = 0.42?
{a} For each row and column total in the ab