A textbook of Computer Based Numerical and Statiscal Techniques part 53 ppsx
A textbook of Computer Based Numerical and Statiscal Techniques part 53 ppsx
... mean µ and variance σ
2
. Then sample
mean
X
di
and variance (S
2
) are
x
= –
1
1
n
i
i
x
n
=
∑
and S
2
=
1
n
xx
i
i
n
−
=
∑
bg
2
1
Also, the standard error of mean of a random sample of ... that the insurance agent’s claim that the average age of
policyholders who insure through him is less than the average for all agents, is valid.
Example 21. A normal population has...
A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx
... problems. A major
advantage for numerical technique is that a numerical answer can be obtained even when a
problem has no analytical solution. However, result from numerical analysis is an approximation,
in ... significant figures at each step of
computation. At each step of computations, retain at least one more significant figure
than that given in the data, perform the last...
A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... 3
Hence maximum percentage error (E
p
)
max
= 11.667%.
Example 26. How accurately should the length and time of vibration of a pendulum should be
measured in order that the computed value of g is ... 4008 and 30.4647 + 0.0639 =
30.5286.
Example 12. Find the product of 346.1 and 865.2 and state how many figures of the result are
trustworthy, given that the numbers are corr...
A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... roots of the equation, obtained by
x
1
=
2
22
44
and
22
bb ac bb ac
aa
−+ − −− −
=x
These are called closed form solution. Similar formulae are also available for cubic and
biquadratic polynomial ... 26
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction,
multiplication, and div...
A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx
... 122
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 22. Evaluate: ∆
n
[sin (ax + b)]
Sol. We know
f∆
(x) = f(x + h) – f (x) therefore
∆
sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... hD hD
hD
116
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 14. Evaluate the following:
I. ∆
2
(cos 2x)
II. ∆
2
(3e
x
)
III. ∆ tan
–1
x
IV. ∆(x + cos x)
the inte...
A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... Suppose
for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given.
140
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Sol. For the given data, difference table is:
∆∆ ∆ ∆
−
−
−
−
−
−
∆
∆
∆∆
∆
∆∆
∆
∆
234
3
2
2
3
3
43
2
54
3
54
2
65
6
7
01
2
11 ... 0f−+×−×+=
138
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
i.e., 4f(3) = 124
i.e., f(3)...
A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... R.H.S.
3.9 FACTORIAL NOTATIONS
The product of n consecutive factors each at a constant difference and the first factor being x is
called a factorial function or a factorial polynomial of degree n and ... L.H.S.
150
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
CorCor
CorCor
Cor
ollary:ollary:
ollary:ollary:
ollary:
To show that,
()
n
n
x
∆
= n! h
n
and
1n+
∆...
A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx
... y
–5
)
228
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 3. Find f(x) as a polynomial of x if
x :–10367
f(x) : 3 –6 39 822 1611
Sol. Now from Lagrange’s interpolation formula,
P(x) ... interpolation formula.
Sol. We are given
()
:78910
:311 9
x
fx
226
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 1. Using Lagrange’s formula, find the value...
A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx
... (5)
244
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 10. Show that the sum of Lagrangian co-efficients is unity.
Sol. Let
()
x
∏
=
()
()
()
01
n
xx xx xx
−− −
The reciprocal of ... 12.46
x
fx
[Ans. 8.337]
242
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 7. Find the value of x correct to one decimal place for which y = 7
Given
x:1 3 4...
A textbook of Computer Based Numerical and Statiscal Techniques part 29 ppsx
... co-efficients a
1
, a
2
a
n
will produce little
error for small x near zero. But probably substantial error near the ends of the interval
268
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
7. Apply ... approximation to a given function.
For evaluating a function f(x) on a computer it is generally more efficient of space and time
to have an analytic approxi...
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