1.
2.
3.
B.SC-III 'C'
ASSIGNMENT
State and prove Fundamental theorem of Difference Calculus.
ch
ch   

Prove that  cos cx  d   2 sin . cos  cx  d 
.
2
2 

Given u 0  u8  1.9243, u1  u 7  1.9590
u 2  u 6  1.9823, u 3  u 5  1.9956
4.
find u 4.
State and prove New ton-Gregory formula for forward interpolation.
5.
Given sin 45   0.7071, sin 50   0.7660
sin 55   0.8192, sin 60   0.8660
find sin 52  by using New ton's formula for forward interpolation.
6.
Prove that divided differences are symmetric functions of their
arguments.
7.
Find the polynomial of the lowest possible degree which assumes the
values 3, 2, 1, -1 respectively.
8.
State and prove Lagrange's interpolation formula.
9.
By means of Lagrange's formula, prove that
y 3  0.05 y 0  y 6   0.3 y1  y 5   0.75 y 2  y 4 
10.
State and prove Gauss Backward interpolation formula.
11.
Apply Bessel's formula to obtain y 25 , given
y 20  2854, y 24  3162, y 28  3544, y 32  3992.
12.
There are 6% defective items in a large bulk of items. Find the
probability that a sample of 8 items will include not more than one
defective item.
13.
Define Binomial distribution. Find its mean and variance.
14.
Find the probability that almost 3 defective fuses will be found in a box
of 200 fuses if experience shows that 2% of such fuses are defective.
(Take e  4  0.0813 )
15.
Fit a Poisson distribution to the following data:
x:
0
1
2
3
4
f :
123
59
14
3
1