Mathematical Models and Statistical Techniques

Mathematical Models and
Statistical Techniques

Table of Contents
PART 1............................................................................................................................................1
PART 2............................................................................................................................................7

PART 1
(a) Given,
P = V2/R
here, unit of power P is watt (joules per sec)
unit of voltage V is volts and,
unit of resistance is ohm
in dimensional form,
P = m2.kg.sec-3
= L2 M1T-3
and,
V = m2.kg.sec-3 .A-1
= L2 M1T-3
then,
R = V2/P
= (L2 M1T-3 .A-1)2
(L2 M1T-3)
= L2 M1T-3 A-2
= m2.kg.sec-3 A-2
(b) t = 2π √m3l
F
here, m is mass,
l is length and,
F is tension
in dimensional form,
F = m x g
= m.kg.sec-2
= L1 M1T-2
then,
1

dimension of t as per given formula –
t = √M3L1
L1 M1T-2
= √M2T2
= MT = kg sec
which is mathematically wrong, therefore, given formula of period of vibration (t) is incorrect.
(c) Given, samples of voltage = 2, 4, 6, ... 40
using arithmetic series formula –
Sn = n [a + l]
2
here, n is no. of terms
a is first term
l is last term
in given sample,
a = 2, n = 20 and l = 40
Sum of 20 voltage samples =
Sn = n [a + l]
2
Sn = 20 [2 + 40]
2
= 10 x 42 = 420 mV
(d) Given, sequence = 1024, 2048, 4096, 8192 ...
using geometric series formula –
Tn = a. rn-1
here, n is no. of terms
a is first term
r is ratio of succeeding and preceding term (II/I)
in given series,
a = 1024 and r = 2048/1024 = 2
2