
SOLVED QUESTION PAPER OF SESSION :
2010-2011
SUBMITTED TO:
Ms. Bikramjeet Kaur
SUBMITTED BY :
Bavanpreet Singh
Roll No. :171
Manveen Kaur
Roll no. : 172
DETERMINANT



A determinant is always
a square
Determinant has a
definite value
Two vertical lines are
used to denote
determinants
MATRIX



A matrix may be
rectangular or a square
A matrix has no definite
value
We use square brackets
to denote matrix
1.Regression coefficients
Just as there are two regression equations
,similarly there are two regression coefficients
.regression coefficient measures the average
change in the value of one variable for a unit
change in value of another variable.
Regression coefficient of X on Y :this coefficient
shows that with a unit change in the value of X
,what will be the average change in the value of
Y.
byx=r. deviation of x
deviation of y
(1)
(2)Regression coefficient of X on Y :this coefficient
shows that with a unit change in the value of X,
what will be the average change in the value of
X.
Bxy=r.deviation of x
deviation of y
2.Regression lines
The regression line shows the average relationship
between two variables . This is also known as the
line of best fit on the basis of regression line , we
can predict the value of a dependent variable .
(1):Regression line of X on Y:the regression line of X
and Y gives the best estimate for the value of X
for any given value of Y .
(2):Regression line of Y on X:the regression line of
Y on X gives the best estimate for the value of
Y for any given value of X.
SIMPLE RANDOM SAMPLING
STRATIFIED RANDOM SAMPLING
It is that method in which
each item of universe has
an equal chance of being
selected in the sample.
Which item will put in
sample and which not ,
such decision is not made
by an investigator on his
will but selection of units
is left on chance.
This method is used when
units of universe are
hetrogenous rather than
homogenous . under this
method , first of all units
of the population are
divided into different
strata in accordance with
their characterstics . then
the samples are selected
on random basis.

(d).Show that 1 a bc
1 b ca =(b-c)(c-a)(a-b)
1 c ab
Sol. Operating r₂-r₂-r₁-r₃-r₃-r₁
1 a bc
1 a bc
1 b ca = 0 b-c ca-bc
1 c ab
0c-a ab-bc
Expanding along c₁, we get
=(a-b)(c-a)(b-c)=(a-b)(b-c)(c-a)
Simple interest for 1.5 years =₹150
Simple interest for 1 year = 150X²/₃ =100
Now , C.I. For 1st year =S.I. Of the 1st year=₹100
153.33-100=₹ 53.33
=C.I. For remaining ⅟₂years-S.I. For ⅟₂years
=₹53.33-₹50=₹3.33
Rate =3.33 X 100 =6.66%
100X ⅟₂
ƩX=NX
N=75,X=27
ƩX=75X27=2025
CORRECTED ƩX=2025-43+53=2035
C0RRECTED X=2035/75=27.13
X
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
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



0.5
1.0
3.0
5-7
7-10
10-15
15-20
20-25
F








2
3
2
4
4
12
6
2
Make equal intervals
Class
interval
s
0-5
5-10
10-15
15-20
20-25
f
7
8
12
6
2
Class
intervals
f
M.V.
fX
c.f.
0-5
7
2.5
17.5
7
5-10
8
7.5
60.0
15
10-15
12
12.5
150.0
27
15-20
6
17.5
105.0
33
20-25
2
22.5
45.0
35
N=35
377.5
X=ƩfX =377.5 =10.79
N
35
Median=17.5th item
Median class=10-15
M=10+17.5-15X5=11.041
12
Modal class:10-15
Z=l₁ + f₁+f₀ X i
2f₁-f₀-f₂
X=10.79,M=11.04,Z=12
Ques : Calculate chain base index numbers
chained to 2003 from the average price of
following three commodities:
Commodi
ties
2003
2004
2005
2006
2007
Wheat
4
6
8
10
12
Rice
16
20
24
30
36
Sugar
8
10
16
20
24
Commodit
ies
2003
p₀
LR
Wheat
4
2004
p₁
LR
6
100
2005
p₂
LR
2007
p₄
LR
150
8
133.3 10
125
12
120
120
30
125
36
120
160 20
125
24
120
Rice
16
100 20
125
24
Sugar
8
100
125
16
10
2006
p₃
LR
Total
300
400
413
375
360
AV of LR
100
133.3
137
125
120
CBI
100
133.3
183
228
274
year
2001
product 77
ion
2001
2003
2004
2005
2006
2007
88
94
85
91
98
90
year
Y
X
XY
X²
2001
77
-3
-231
9
2002
88
-2
-176
4
2003
94
-1
-94
1
2004
85
0
0
0
Ques : Below are given the figures of production
of sugar factory:
(a)Fit a straight line by the least squares method
and tabulate the trend values.
(b)Eliminate the trend . What components of the
series are thus left over?
(c)What is monthly increase in the production of
sugar?
2005
91
+1
91
1
2006
98
+2
196
4
2007
90
+3
270
9
N=7
ƩY=623
Ʃx=0
ƩXY=56
The equation of straight line curve is
Y=a+bX
a=ƩY=89
N
b=ƩXY=2
ƩX²
ƩX²=28
Y = 89 = 2X origin:2004, X unit = 1 year
 Calculation of trend values
For 2001, X = -3
2002, X = -2
2003, X = -1
2004, X = 0
2005, X = +1
2006, X = +2
2007, X = +3
(b). Elimination of trend
Year
2001
2002
2003
2004
2005
2006
2007
Y
77
88
94
85
91
98
90
Y
83
85
87
89
91
93
95
Y-Y
-6
3
7
-4
0
5
-5
(c).Monthly increase = b = 2 = 0.166
12 12
= 166.66 tonnes.
Ques : A computer while calculating the
correlation coefficient between two variables X
and Y from 25 pairs of observation obtained
from following results :
N = 25 ƩX = 125 ƩX² = 650
Ʃy = 100 Ʃy² = 460 Ʃxy = 508
Incorrect
correct
X Y
X Y
6 14
8 12
8 6
6 8
Correct ƩX = 125 - 6 – 8 + 6 = 125
Correct ƩY = 100 - 14 - 6 + 12 + 8= 100
Correct ƩX² = 436
Correct ƩY² = 520
Correct ƩXY = 520
r = 0.667
Ques: the following data relates to the scores
obtained by a salesman of a company in an
intelligence test and their weekly sales in
thousand rupees :
intell
igenc
e
A
B
C
D
E
F
G
H
I
Test
score
s
50
60
50
60
80
50
80
40
70
Week 30
ly
sales
60
40
50
60
30
70
50
60
(a). Obtain the regression equation of sales on
intelligence test scores of the salesman.
(b). If he intelligence test scores of a salesman is
65, what would be his expected weekly sales?
X
x
x²
Y
y
y²
xy
50
-10
100
30
-20
400
200
60
0
0
60
10
100
0
50
-10
100
40
-10
100
100
60
0
0
50
0
0
0
80
20
400
60
10
100
200
50
-10
100
30
-20
400
200
80
20
400
70
20
400
400
40
-20
400
50
0
0
0
70
10
100
60
10
100
200
ƩX=540
Ʃx=0
Ʃx²=1600
ƩY=450
Ʃy=0
Ʃy²=1600
Ʃxy=1200
X = 60 , Y = 50
Byx = 0.75
Regression equation of Y and X
Y= 50 + 0.75X
(b). For X = 65 , Y₆₅ = 50 + 0.75(65) =53.75
Ques : 12 dice were thrown 4096 times . Each 4,5
or 6 spot appearing was considered to be a
success . while 1,2 or 3 spot was a failure
calculate the theoretical frequencies for
0,1,2,....,12 successes.
Solution :
N = 12 , P = probability of success
N = =4096
The probability of 0,1,2,....,12 will be given by
P(X)ᶰCᵪq = ᶰ-ᵡpᵡ for n = 1,2,3,...,12.
The expected frequencies are obtained by
increasing the probability by N as follows :
X
fe9x0 = N .ᶰ Cᵪ q ᶰ-ᵡpᵡ
1
1
2
12
3
66
4
220
5
495
6
792
7
924
8
792
9
495
10
220
11
66
12
12
Total
4096