a)

b)

a)

(b)

९)

2)

b)

९)

2)

b)

९)

02000MA204052001

९ (८1, ८2) = 5 + 367931ಓ-ಓಿ| , Find the mean, variance and the covariance of the

random variables X(4) and X(6).

The joint PDF of X,Y is f(x, y) = kxye~@°+¥7), x > 0; y > 0. Find the value
of k, marginal distributions of X,Y and check whether ೫, Y are independent.

Let {X(t) = Acos wt + Bsinwt , £ > 0} be arandom process where A and B are
independent random variables following normal distribution with mean 0 and
variance 4. Check whether {> (६) } is WSS.

PART C

Answer any two questions
Is the Poisson Process a stationary process? Find the Autocorrelation of the Poisson

process.
0.2 03 0.5

The tpm of a Markov chain with states 1,2,3 is P=]0.1 0.6 0.3] and the initial
04 03 03

distribution is P(0)= (0.5,0.3,0.2). Find (0206) = 2 (ii) P(X3 = 3,X2 =2,X, =
1,2 = 3)

0.5 0.5

01 0 al: Find the steady state distribution of

The tpm of a Markov chain is P = ۱

the process.

Use Newton’s forward difference formula to find y at x = 1.5.

Use Euler’s method with h = 0.025 to compute the value of y(0.1) for the
differential equation y’ = 2 - 22, y(0) = 1.

Use Newton-Raphson method to find 1/35 correct to 4 decimal places.

A man either drives a car or catches a train to go to office every day. He never goes
two days in a row by train. But if he drives one day then the next day he is just as
likely to drive again as he is to travel by train. On the first day of a week, the man
tosses a fair dice and drives to work if he gets a 6. Find the Probability that (i) he
takes train on second day (ii) he drives to work on third day (iii) he drives to work in
the long run.

Find the Lagrange’s Interpolating polynomial corresponding to given data:

f (0) =0,f(1) = 1, (2) = 20. Hence find / (1.5)

Evaluate | നോ dx using Trapezoidal rule with h = 0.25

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