b)

a)

b)

0)

6)

84/0102

x 0.5 1.0 1.5 2.0 2.5

Find f (0.7) using suitable form of Newton’s interpolation formula.

Use Runge-Kutta fourth order method to find y(0.2)and y(0.4), given the initial
value problem = =e*+y, y(0)=0

Find the probability distribution of the time between two consecutive arrivals in a
Poisson process.

A machine is in one of two states (i) down (state 0) or (ii) up (state 1). The transition
probabilities between the states is given by the following matrix (TPM)

0.75 5
0.40 0.60

Find the proportion of time the machine will be up in the long run.
Find the real root of f(x) = e?* — x — 6 lying between 0 and 1 using Newton-

Raphson method.

Evaluate 18 ௪35/2 dx numerically using Simpson’s rule with a suitable step-size.

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