West Bengal Institute of Technology (WBIT) 2008 M.C.A MM301 Statics and Numerical Techniques ( ) - Question Paper
C*/lit58a-3/MCMCA)-301/08/(09) 3
* C,'*' ' . ' . ' -
ENGINEERING & MANAGEMENT EXAMINATIONS, DECEMBER - 2008
STATISTICS AND NUMERICAL TECHNIQUES
Time : 3 Hours 1 ~ ' (Full Marks : 70
Graph sheets are provided at the end of the booklfet. >
GROUP - A ( Multiple Choice Type Questions) ,
1. Choose the correct alternatives for any ten of the following : 10x1 = 10
i) Two unbiased coins are tossfed. What is the probability of obtaining3 heads* ?
<> 2 b> 3
c) | d) 0.
H) If x be the arithmetic mean of the values x t weighted by ft (C = 1, 2....... n ),
then
i = 1
. a) True b) False.
ill) What is the Standard Error of the sample mean for a random sample of size n drawn with replacement ( o =>s.d., N = population size, n = sample size ) ?
a) b)
4n V JV - 1 'fn
, VN- n ' JV - n
c) o irrr d) a -=
JV-i t V
iv) What is the probability that a leap year selected at random contains 53 Sundays ? '
, 1 ,. 2 a> b)
366 366
, 2 3
c) 7 d) y .
CS/MCA/SEM-3/M(MCA)-301/08/(09)
v) For two events A, B, PttB / . r
et &tm\/P(B) b) P(AB)/ftA$
c) P( B) / P[ A) d) J*fA) * P(B) . 1
vl) The number of significant figures in 0*0128742 is
a) five b) six
c) seven d) three. _
' vii) If/( x) is a polynomial of degree n, the n* order difference is a constant, v a) True' b) False. - _
viii) Relation between mean and variance of a random variable following binomial distribution is
a) Mean- Variance b) Mean > Variance
c) Mean < Variance <|) Mean * Variance2. _
' / ' ; '
. . . . .
ix) For a distribution, mean, median and mode are found to be equal. What kind of
distribution is the most possibility ?
a) Binomial b) Poisson
c) Normal d) Geometric.
x) The truncation error in Composite Trapezoidal Rule is
a) h2 b) h3
c) h4 dj nope of these. _
xi) If a is the actual value and e is the estimated value, the formula for relative error is
a) a/e b) (a-e)le
c) | a - e | / a d) { a - e J / e. |
33191 (4/tail
' ; v
xU) If the random variable X has p.d.f. /( x) = \ x. 0 x % find the mean value ofX. ,
' 4 -.7
a)
b)
d)
8
i 5 c) 4
2
3
xiii) The relation between shift operator 'E' and forward difference operator A' Is given by
a) A = I + e c) E = A
b)
d}
E- 1 + A E~ A + 2.
xiv) When the variance of a random variable is |, the Var ( 3X + 5 ) Is
a) 6 c) 11
b)
d)
none of these.
GROUP -B ( Short Answer Type Questions)
Answer any three of the following.
3 x 5 = 15
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2. Find the missing frequencies in the following frequency distribution, when It is known that A.M. = 11-09 and total frequency = 60 : * | ||||||||||||||||||
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1 |
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6. Find y1 at 0-45 from the following data : | ||||||||||||
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Fit a linear equation to the following data : | ||||||||||||
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GROUP -C ( Long Answer Type Questions )
Answer any three of the following.
3x 15 = 45
8. a) There are two boxes, the first containing 3 white and 7 black balls and the
second containing 7 white and 3 black balls. One box Is chosen at random and from it 2 balls are drawn without replacement. Find the probability that both the balls are white. Also, given that both the balls are white, find the conditional probability tha,t the first ball was chosen.
*.
b) Prove that In the limiting case. Binomial distribution tends to Poisson distribution.
c) Prove that for two events E j and B2 ,
+-
P(IUE2)=P(1) + P(E2)-P(ElnE2). 5 + 5 + 5
9. a) Prove that P ( A c ) = 1 - P {A ), where A c Implies complement of the event A.
b) Find the probability of getting exactly two erven numbers when a balanced die Is rolled thrice.
c) Prove that for a Binomial distribution, mean Is greater than variance. 4 + 5 + 6
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10. a) The number of telephone calls received in 245 successive one minute intervals at an exchange are shown in the following frequency distribution : | ||||||||||||||||
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Evaluate the mean and mode,
b) Compute the Standard Deviation from the following distribution of marks
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obtained by 90 students : | ||||||||||||||||
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c) Find the median and median class of the following data given below : | ||||||||||||||
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15
11. a) Given :
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X: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
fix) |
1 |
8 |
27 |
64 |
125 |
216 |
343 |
512 |
Construct the difference table and compute (1) /( 1-5) and (ii) /( 7-5 ).
b) Given the following data, find / ( x ) assuming it to be a polynomial of three degree In x. ,
|
X: |
0 |
1 |
2 |
3 |
|
fix) |
1 |
2 |
il |
34 |
c) Find a positive root of x + In x - 2 = 0, by Newton-Raphson method, correct to six significant figures. 1F
C8/lSCA/8Ell-3/M(MCA}-301/08/(09)
12. a) Solve the following system
8
2Xj - 3x2 + 4x 3 = 8
X l * X2 + 4x3 =
3x 1 + 4x2 - x3 = 8
by LU-factorization, method.
Solve by Euler's modified method, the following differential equation for x = 0-02, by taking step length h ** 0*01, dy
b)
= x2 + y, y * 1 when x = 0.
dx
c) Find the positive roots of the equation x3 - 3x + 106 = 0, by method of bisection, correct to three decimal places 15
END
93131 (4/12) j
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Attachment: |
| Earning: Approval pending. |
