Download PTU B.Tech 2020 March ECE 3rd Sem BTAM 303 18 Mathematics Iii Question Paper

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Roll No. HEEEEEEEEEE Total No. of Pages : 03
Total No. of Questions : 09

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1. Write briefly :
   1. In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times frequency corresponding to 4 successes. Find the standard deviation of the distribution.
   2. Find the Z-transform of ¢ sin 2¢
   3. Find the Laplace transform of £ sin 1
   4. Define Binomial and Poisson distribution functions.
   5. Define Rank correlation.

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   6. Define the Laplace and Fourier transforms.
   7. Define unit-step and dirac delta functions.
   8. Define discrete and continuous random variables.
   9. State convolution theorem of Fourier transform.
   10. Given that f (x):k(EJ , 1s a probability distribution for a random variable which can take on its values x =0, 1, 2, 3, 4, 5, 6. Find .

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SECTION-B

2. Use Laplace transform method to solve
   d’x 2dx ,
   

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   darr dt
   withx =2, @z—l att=0.
   dt
3. Find the Fourier sine transform of ¢'*!. Hence show that :
   © X sinmx e "
   

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   J' > = ,m>0
   0 1+x 2
   2
4. If U(n)=2E 24
   (z-1)
   

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   Evaluate u, and u;.
5. The theory predicts the proportion of beans, in the-four groups A, B, C and D should be 9:3:3:1. In an experiment among 1600 beans, the. numbers in the four groups were 882, 313, 287 and 118. Does the experimental result support the theory?
   (The table value of x> for 3 d.f. at 5% level.of significance is 7.81).
6. The two regression equations of the. variables x and y are x = 19.13 — 0.87y and y=11.64-0.50 x. Find
   1. mean of x and y
   2. the correlation co-efficient between x and y.

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SECTION-C

7. Find the Fourier cosine series of the function f(x) = © —x in 0 >l .m
   Z(2r+1)? 8
8. 1. Marks obtained by a number of students are assumed to be normal distributed with mean 50 and variance 36. If 4 students are taken at random, what is the probability that exactly two of them will have marks over 657
      

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      Given that | 02®(z)dz=0,4772 where Z is N (0, 1).
   2. Fit the second degree parabola to the following data :
      

      X	0	1	2	3	4
      Y	1	1.8	1.3	25	63

9. From the given data, find (i) the two regression equations, (ii) the coefficient of correlation between the marks in Mathematics & Statistics, and (iii) the most likely marks in Statistics when the marks in Mathematics are 30.
   

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   Marks in Mathematics	25	38	35	32	31	36	29	38	34	32
   Marks in Statistics	43	46	49	41	36	32	31	30	33	39

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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