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Showing posts with label MCSE-004. Show all posts
Showing posts with label MCSE-004. Show all posts
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Perform the following:
a)  What is the utility of residual plot ? what are its disadvantages ?
b)  Given Equations of two lines of regression are : 4x+ 3y+ 7 = 0 and 3x+4y + 8 = 0 . Find: 
(i) mean of x and mean of y 
(ii) Regression coefficient of b yx, and bxy
(iii) Correlation coefficient between x and y 
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Perform The following
a)  If a bank receives on an average λ=6 bad cheques per day what is the  probability that it will receive 4 bad cheques on any given day. 

  b)  A farmer buys a quantity of cabbage seeds from a company that  claims that approximately 90% of the seeds will germinate if planted  properly. If four seeds are planted, what is the probability that  exactly two will germinate.

A)
Let X denote the number of bad cheques received by the bank in a day with average number of such cheques being 6 i.e.E(X)=6. We can use Poisson distribution to model the uncertainty in such cases i.e. X∼Pois(6). So the probability that X is equal to 4 is
Pr(X=4)=64e−64!
To get this value, one can use R:
    

  1. x = 4
    2. 

  2. lambda = 6
    3. 

  3. dpois(x, lambda)
    4.


and the value is:


Pr(X=4)=0.1338526


B) 

 This situation follows the binomial distribution with n=4 and p=90/100=9/10
The random variable X is the number of seeds that germinate. We have to calculate the probability that exactly two of the four seedswill germinate. That is P[X=2]. By applying Binomial formula , we get
 P[X=2] = (4C2) * (9/10)2 *(1/10)2
 = 6 * (81/100) * (1/100) = 486/10000 = 0.0486
So , the required probability is 0.0486 

Perform the following:
 a)  Estimate Y(0.4) by the Classical Runge-Kutta method when  Y¢(x)=X 2 +Y 2 , Y(0)=0 & h = 0.2.  b)  Given   ; with initial condition y=1 at x=0. Find y  approximately at x=0.1; using Euler’s Method  
c)  Solve the given Differential Equation   ;  with initial  condition y(0)=1. Using Fourth Order Runge-Kutta method from t=0  to t=0.4 taking h=0.1 
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Perform The following:
 a)  Calculate the value of integral I = ∫ + 6 4 3 2 x by h=0.5 ; by Using 
 i)  Simpson 3/8 rule  ii)  Weddle’s rule 
 iii) Simpson 1/3 rule  iv)  Trapezoidal rule 
 b)  Compute the integral  ∫ + = 2 1 2 1 2 dx x x I by applying Gauss’s Quadrature  formula. 
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Perform the following :
 a)  Find Newtons Forward Difference interpolating Polynomial for the  following data  X :  0.1  0.2  0.3  0.4  0.5 F(X) :    1.40  1.56  1.76  2.00  2.28
b)  Estimate the missing term in the following data, using Difference table 
x :   1   2   3   4  5 
f(x) :    3   7  ?   21   31
Perform the Following:
a)  Solve the following systems of equations
2X + 8 Y –2 Z = -10; X + Y – 6 Z = -12; 6 X– 2Y – 2Z = -18 
i)  Using the Gauss elimination method 
ii)  Using LU Decomposition method 
iii)  Discuss the pitfalls of Gauss Elimination method. 
b)  Solve the following system of equations: 
x + y - 2 = 0 ; - x + 3 y = 2; x - 2z = - 3 
Using Jacobi Method and Gauss Seidel method. Assumethe initial 
solution vector [0.8 0.8 2.1]
T
. 
Write a short note on Secant method, Regula Falsi method and the  Newton Raphson method and further discuss their relative advantages  and disadvantages. Determine the efficiency or the  order of these three  methods? Using Secant method, Regula Falsi method and the Newton  Raphson method, find the real-root of the equation X 3  – X 2  – 2 = 0 
How Error differs from Uncertainty. Briefly discussthe classification of  errors. If  π=22/7 , is approximated as 3.14, find the absoluteerror  relative error and relative percentage error. Expla in the term Accuracy  and Precision with suitable example. 
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