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Unformatted text preview: National Institute of Technology-Rourkela % § 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 «a R, defined by X(l) = 1; X(Z) = 2; X(3) = 3; X(4) : 4; X(5) = 5; X(G) = 6. Then find 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 find 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: laiiii‘lhi l'éléi‘ii 132i 256i Hence, obtain the interpolating polynomial that fits the above data. [Bl . Use bisection method to obtain a root of the equation, f (1:) = 00590 — are” = 0. in the interval [0,1] correct upto 4—decimal places. [3] . Find the positive root of f(x) 2: a: — 0.2 sin a: — 0.8 =2 O accurate upto 4—decimals, by using Newton—Raphson method. [3] . interpolate f(0) = 1, f(1) = 0, f(2) = —1. f(3) : 0 by cubic spline satisfying to 2 U and k3 = —6. [3] Approximate f(:r) by a suitable polynomial to show fab f(ar)dac a 3% [f0 +3)“1 + 3f2 + f3], Where f<$i) = fi- l3l *******END******* ...
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