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Saturday, April 1, 2017

KTU B.TECH S4 MODEL QUESTIONS PROBABILITY DISTRIBUTIONS,TRANSFORMS AND NUMERICAL METHODS




KTU B.TECH S4 MODEL QUESTIONS PROBABILITY DISTRIBUTIONS,TRANSFORMS AND NUMERICAL METHODS 




PART 1

1. (a) Check whether the functionKTU B.TECH S4 MODEL QUESTIONS PROBABILITY DISTRIBUTIONS,TRANSFORMS AND NUMERICAL METHODS [ PDTM ] MA202 | QUESTION BANK | IMPORTANT QUESTIONS - |can serve as probability distribution. 


(2) (b) Given thatKTU B.TECH S4 MODEL QUESTIONS PROBABILITY DISTRIBUTIONS,TRANSFORMS AND NUMERICAL METHODS [ PDTM ] MA202 | QUESTION BANK | IMPORTANT QUESTIONS - |is a probability distribution. Find k.


2. Derive mean of a binomial distribution. 


3. During one stage in the manufacture of integral circuit chips a coating must be applied. If 70% chips receive a thick enough coating, find probabilities that among 15 chips 


(a) atleast 12 will have thick enough coating. 


(b) atmost 6 will have thick enough coating. 


(c) exactly 10 will have thick enough coating. 


4. Find the positive solution of 2sinx=x using Newton-Raphson method. 


5. Use Newton-Raphson method to find a root of the equation x^3-2x-5=0.


6. (a) Given f(2)=9 and f(6)=17. Find an approximate value of f(5) by linear Lagrange’s interpolation.


(b) Compute an approximate value of ln 9.2 correct to 4 decimal places from ln 9.0=2.1972 and ln 9.5=2.2513 by linear Lagrange interpolation.





Part 2


1. Check whetherKTU B.Tech S4 Question Papers For Probability Distributions,Transforms And Numerical Methods [ PDTM ] MA202 | Question Bank | Important Questions - ||can define probability distribution. Explain. 


KTU B.Tech S4 Question Papers For Probability Distributions,Transforms And Numerical Methods [ PDTM ] MA202 | Question Bank | Important Questions - ||

2. Find mean and Variance for the following probability distribution:


3. If the probability is 0.05 that a certain wide-flange column will fail under a given axial load, what are the probabilities that among 16 such columns, 


i) At most 2 will fail 


ii) At least 4 will fail 


4. Design a Newton’s-Raphson formula to find cube root of a given positive number and apply it for C = 7, X= 2. 


5. Apply Newton-Raphson Method to the equation f(x ) = x^3+ x− 1 = 0, (Four Iteration).



6. State the conditions for Poisson approximation to Binomial distribution. Approximate Binomial distribution as Poisson . 

OR 

7. i) The probability that a person suffers bad reaction due to a certain injection is 0.001. 


Determine out of 2000 individuals, the probability of exactly 3 will suffer the bad reaction and probability of more than 2 will suffer bad reaction. 


ii) The probability that a bomb dropped from a plane will hit the target is 1/5. If 6 bombs are dropped , find the probability of exactly 2 will strike the target and probability of at least 2 will strike the target.


8.Given f(32) = 0.5299, f(35) = 0.5736, f(38) = 0.6157, f(41) = 0.6561, f(44) = 0.6947. Find f(42) and f(43) using Interpolation.


9. Using Langrange’s formula, fit a polynomial for the following data.

x:1 2 7 8
 y:4 5 5 4 

Find the value of when = 6.



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