KTU B.Tech S4 model Questions for Probability distributions, Transforms, and Numerical Methods
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FOURTH SEMESTER B.TECH DEGREE EXAMINATION
MA202 Probability distributions, Transforms and Numerical Methods
Time: 3 Hrs Marks: 100
( Answer any two )
a) check whether the following can serve as probability distribution and why?
f (x)=x2/25 where x=0,1,2,3,4 (5 Marks)
(b)Give the probability mass function
x 0 1 2 3
P(x) 0.1 0.3 0.5 0.1
Find mean , variance and V(2X-5)(5 marks)
(c) 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) atmost 2 will fail (ii) atleast 4 will fail
b) If X is a binomially distributed random variables with mean 2 and variance 4/3.
(c) A binomial distribution with parameter n=5 satisfies the property 8P(X=4) =P(X=2).Find the value of p and P(X>1)
(a) It has been claimed that in 60% of all solar-heat installations the utility bill is reduced by at least one-third. Accordingly, what are the probabilities that the utility bill will be reduced by at least one-third in
(i) four of 5 installations.
(ii) At least four of 5 installations (7 Marks)
(b) It is known that 5% of the books bound at a certain bindary have defective bindings. Find the probability that 2 of 100 books bound by this bindary will have defective binding using
(i) The formula for the binomial distribution
(ii) The Poisson approximation to binomial distribution. (8 marks)
(Answer any two)
c) Express the differential equation in Laplace transformation form
6 a) Obtain the Fourier sin transform of
b)Obtain the inverse cosine transform of e-s.
( Answer any two )
7 a) Find the positive solution of 2sinx = x using Newton-Raphson method
b) Use Newton-Raphson method to find a root of the equation x3-2x-5 = 0.
c)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 y when = 6.
8 a) Using Newton’s Forward Difference formula estimate the value of f(15)from the following data
x : 10 20 30 40 50
f(x) : 46 66 81 93 101
b) Using Newton’s backward Difference Interpolation formula, estimate the value
(42)from the following data.
x : 20 25 30 35 40 45
f(x) : 35.4 33.2 29.1 26.0 23.1 20.4
9 a) Solve the following system of equations by Gauss elimination method with partial pivoting.
b)Find Solve the following system by Gauss elimination (i) without pivoting (ii) with partial pivoting.
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