A textbook of Computer Based Numerical and Statiscal Techniques part 42 potx
A textbook of Computer Based Numerical and Statiscal Techniques part 42 potx
... normal equations are given by
2
0
S
ynab x
a
∂
=⇒ = +
∂
∑∑
(1)
224
0
S
xy a x b x
b
∂
=⇒ = +
∂
∑∑∑
(2)
404
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Here
6n =
Normal equations are,
17.25573 ... =
∑
x
2
300
=
∑
xY
∑
Substituting the values of
x
∑
, etc. and calculated by means of above table in the normal
equations. We get,
5.7536 = 5A + 34B
and 40.8862 = 3...
A textbook of Computer Based Numerical and Statiscal Techniques part 7 potx
... 1.4036
0.10203
=
Since, x
3
and x
4
are approximately the same upto four places of decimal, hence the required
root of the given equation is 1.4036.
48
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Using ... between 1.6866 and 2.
50
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
and f(3) = (3)
3
– 2(3) – 5 = 16
Therefore, a root lies betw...
A textbook of Computer Based Numerical and Statiscal Techniques part 28 potx
... (0,0) and (4,2) and tangent to the lines y = 0 and y = 2 as shown in the figure. Apply Hermite’s
interpolation formula to obtain this polynomial
Sol. Since tangents are parallel to X-axis,
y′ = 0 ... (1.05) = 0 .420 735 + 0.445605 + 0.00675375 – 0.00567
sin (1.05) = 0.86 742. Ans.
Example 4. A switching path between parallel railroad tracks is to be a cubic polynomial joining
positi...
A textbook of Computer Based Numerical and Statiscal Techniques part 38 potx
...
()
[]
0.05
1. 2428 1. 4428 6.2724 1.6997 1.3997
3
=+ ++ =
364
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
which is same as the predicted value.
∴
60.30
1.3997
yy==
and
6
1.6997
y
′
=
The result can ... differential equation
()
,
dy
yfxy
dx
′
==
by this method we first obtain the approximate value of
1n
y
+
by Predictor formula and then
improve the value of
1n
y...
A textbook of Computer Based Numerical and Statiscal Techniques part 39 potx
... value y
i
and the true value y(x
i
) at any stage is
known as the total error. The total error at any stage is comprised of truncation error and
round-off error.
The most important aspect of ... DIFFERENTIAL EQUATION
371
Inherent stability is determined by the mathematical formulations of the problem and is
dependent on the eigen values of Jacobian Matrix of the differential...
A textbook of Computer Based Numerical and Statiscal Techniques part 54 potx
... sample of 1000 farms in a certain area has a S.D. of 192
kg. Another random sample of 1000 farms gives a S.D. of 224 kg. Are the standard
deviations significantly different?
[Ans. Z = 4.851 and ... 516
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
where
x
1
be the mean of a sample of size n
1
from a population with mean µ
1
and variance σ
1
2.
x...
A textbook of Computer Based Numerical and Statiscal Techniques part 55 potx
... E(c)=
accd
N
++
bgbg
and E(d)=
bdcd
N
++
bgbg
abab
cdcd
ac bd N
+
+
++
∴ χ
2
=
aEa
Ea
bEb
Eb
cEc
Ec
dEd
Ed
––––
af
af
af
af
af
af
af
af
2222
+++
(2)
a – E (a) =a –
abac
N
++
bgbg
=
a a b c d a ac ... than the tabulated value, H
0
is rejected.
i.e., the data are not consistent with the hypothesis that the Binomial law holds and that the
chance of a male birth is not equal to...
A textbook of Computer Based Numerical and Statiscal Techniques part 56 potx
... sample size is less than equal to 30 (≤ 30) and the population
standard deviation is unknown.
Let X
i
, i = 1, 2, , n be a random sample of size n from a normal population with mean
µ and variance ... highly
significant. Hence we reject the null hypothesis.
Example 16. A machinist is making engine parts with axle diameters of 0.700 inch. A random
sample of 10 parts shows a...
A textbook of Computer Based Numerical and Statiscal Techniques part 62 docx
... the Range
Lower limit a = 0
Upper limit b = 6
Enter the number of subintervals = 6
Value of the integral is: 1.3571
598
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Enter the value of y2 ... ALGORITHM FOR TRAPEZOIDAL RULE
Step 1. Start of the program for numerical integration
Step 2. Input the upper and lower limits a and b
Step 3. Obtain the number of sub...
A textbook of Computer Based Numerical and Statiscal Techniques part 1 ppt
... This page
intentionally left
blank
This page
intentionally left
blank
A TEXTBOOK OF
COMPUTER BASED NUMERICAL
AND
STATISTICAL TECHNIQUES
Anju Khandelwal
M.Sc., Ph.D.
Department of Mathematics
SRMS ... Based Numerical and Statistical Techniques is primarily written
according to the unified syllabus of Mathematics for B. Tech. II year and M.C .A. I year students
of...
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