**Unformatted text preview: **National Institute of Technology-Rourkela
% Â§ Department of Mathematics . ' - t ' ' -2012-2013
W ~ Mid Semester Txammation
1091mm: MA 201 Time: 2 hours
nstructions: Full marks: 30 0 Answer all questions. 0 All parts of a question should be answered at one place. 10. . Throw a die once. Let S be the sample space of all possible outcomes. Suppose X is the random variable which denotes the face value, that is X : S Â«a R, deï¬ned
by X(l) = 1; X(Z) = 2; X(3) = 3; X(4) : 4; X(5) = 5; X(G) = 6. Then ï¬nd the
distribution function F(:L') of X. (3] . If X is a Poisson random variable such that, %P(X = 1') = P(X = 3). Find (i) P(X 3 1) (ii) P(X g 3) (iii) p(2 g X g 5). [3} . A continuous random variable X has a probability density function, MK OSxSL
f(:z:) _ { 0, otherwise. Find a and 1) such that, (i) P(X S a) = P(X > a) and (ii) P(X > b) : 0 - 05. [3} . The marks obtained in Mathematics in a certain examination found to be normally distributed. If 15% of the students have secured 60 marks or more and 40% have got
less than 30 marks, then ï¬nd the mean and standard deviation of the distribution. [3i . A bag contains 5 white and 2 black balls and balls are drawn one by one without replacement. What is the probability of drawing the second white ball before the
second black ball? [3] . construct the divided difference table for the following data: laiiiiâ€˜lhi l'Ã©lÃ©iâ€˜ii 132i 256i Hence, obtain the interpolating polynomial that ï¬ts the above data. [Bl . Use bisection method to obtain a root of the equation, f (1:) = 00590 â€” areâ€ = 0. in the interval [0,1] correct upto 4â€”decimal places. [3] . Find the positive root of f(x) 2: a: â€” 0.2 sin a: â€” 0.8 =2 O accurate upto 4â€”decimals, by using Newtonâ€”Raphson method. [3] . interpolate f(0) = 1, f(1) = 0, f(2) = â€”1. f(3) : 0 by cubic spline satisfying to 2 U and k3 = â€”6. [3] Approximate f(:r) by a suitable polynomial to show fab f(ar)dac a 3% [f0 +3)â€œ1 + 3f2 +
f3], Where f<$i) = fi- l3l *******END******* ...

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