JNTUW

ORLD

Code: 13D11101

M.Tech I Semester Regular Examinations February 2014 PROBABILITY & MATHEMATICAL ANALYSIS

(Thermal Science and Energy Systems) (For students admitted in 2013 only)

Time: 3 hours Max Marks: 60

Answer any FIVE questions All questions carry equal marks

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1 List the rules for finding the particular integral. 2 The points of trisection of a string are pulled aside through the same distance an

opposite sides of the position of equilibrium and the string is released from rest. Derive an expression for the displacement of the string at sub sequent time and show that the mid-point of the string always remains at rest.

3 Show that: (a)

(b)

4 State and prove Rodriquezs formula and show that satisfies the differential

equation 5 Given where Find correct to four decimal places.

Using Runge-Kutta second order and Runge-Kutta fourth order. 6 (a) Derive Adma-Bashforth formulaA predictor corrector method. (b) Write standard five point formula. Give the figure with points. 7 (a) State and prove Bayes theorem. (b) The chance that doctor A will diagnose a disease x correctly is 60%. The chance that a

patient will die by his treatment after correct diagnosis is 40% and the chance of death by wrong diagnosis is 70%. A patient of doctor A, who had disease x died. What is the chance that his disease was diagnosed correctly?

8 Give an explanation about linear co-relation coefficient for a Bird rate frequencies

distributions.

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