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D192003

Pages:3

Prove that binomial distribution with parameters n and p can be approximated to

Poisson distribution when n is large and p is small with np = /, a constant.

PART B (MODULES III AND IV)
Answer two full questions.

Use Fourier integral to show that ர்‌

Find the Fourier Sine and Cosine Transform of f(x) = {

Find the Laplace Transform of :
(i) e © sin 3t cos 2t
(ii) t? coswt

(11). t?u(t-1)

Find the inverse Laplace Transform of :

5 1- 75

(1) (s—3)(s—1)(s+2)
we 5-0

(11) In =
7 Ces

5رو-ی )111(

Find the Fourier Sine Transform of f(x) = ©

20 ८०52८ + ८05711८८
1+ 2

18]

0

0 if

Hence evaluate f

dw =< 1/2

76

ifx <0
ifx=0
ifx>0

x? if0O0x>1

wsinxw wsinxe |
2
+

Solve by using Laplace Transform: y" + 2y' — 3y = 6e~7",y(0) = 2, y'(0) - -

PART C (MODULES V AND VI)
Answer two full questions.

Find the positive solution of 2sinx = x using Newton Raphson (method correct to

five decimal places).

Find the value of tan 33° by using Lagrange‘s formula for interpolation

30° 320

38°

A second degree polynomial passes through the points (1,-1) (2,-1) (3, 1) (4, 5).

Find the polynomial f (x), Also find f (1.2).

A river is 80 metre wide. The depth y in metres at a distance x metres from one

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