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The tpm of a Markov Chain is P = | i} Find the steady state distribution of
2 2

the chain.

A radioactive source emits particles at the rate of 6 per minutes in accordance with
Poisson process. Each particle emitted has a probability of त being recorded.
Find the probability that atleast 5 particles are recorded in 5 minutes.

Evaluate ۳ 109५ (2) dX using Simpson’s 12۳" rule. (Take h = 0.2)

Use Newton’s forward interpolation formula to evaluate y(23) from the following

a ண | =| ಇಷ ട്‌ ர | = |
நூ ae | 32.1 ணை | ‏ٹک‎ 22.7 | 21.9 |

Use Runge-Kutta method of order 4 to find (0.2) for the differential equation:

data:

‎उ + 0.5, y(0) 51. (Take 1 = 0.2)‏ = او
‎A house wife buys 3 types of cereals A, B, and C. She never buys the same cereals‏
‎in successive weeks. If she buys cereal A, next week she buys B. However, if she‏
‎buys B or C, next week she is 3 times as likely to buy A as the other cereals. In the‏
‎first week of May she buys cereal C. Then what is the probability that (i) in the‏
‎second week she buys cereal ^ (ii) In the third week she buys cereal C (iii) In‏
‎the long run, how often she buys cereal B.‏

‎Use Lagrange’s interpolation formula to find y(2) from the following table:

‎Evaluate cube root of 41 correct to four decimal places using Newton- Raphson

‎method correct to 4 decimal places.

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