PTU Punjab Technical University B-Tech May 2019 Question Papers 2nd Semester Computer Science Engineering (CSE)
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Roll No.
Total No. of Pages : 04
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 Batch) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-204-18
M.Code : 76257
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION - B & C have FOUR questions each.
3.
Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4.
Select atleast T WO questions from SECT ION - B & C.
SECTION-A
Answer the following :
1)
For two events A and B such that P(A) = ?, P(B) = 1/3 and P(AUB) = ?. Find P(B/A).
2)
If A, B and C are three mutually exclusive and exhaustive events associated with random
3
1
experiments. Find P(A) given that P(B)
P( )
A , P(C) P(B).
2
2
3)
If a random variable X assumes the values 0 and 1 with P (X = 0) = 3 P(X = 1), then find
the variance of X.
4)
The mean of the binomial distribution is 20 and standard deviation is 4. Calculate the
parameter of its distribution.
5)
State Binomial and Poisson distribution.
6)
What is Spearman's rank correlation coefficient?
2
7)
In Poisson frequency distribution, frequency corresponding to 3 successes is
times
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3
frequency corresponding to 4 successes. Find the variance of the distribution.
8)
Let X be the random variable such that P (X = ?2) = P (X = ?1),l P (X = 2) =
P (X = 1) and P(X > 0) = P(X < 0) = P (X = 0). Obtain the probability mass function of x.
9)
State chi-square and Student's t-distributions.
10) A computer program has produced the following output for a hypothesis-testing problem:
Difference in sample means: 2.35 ; Degree of freedom : 18; Test statistics: 2.01. Find the
standard error of the difference in sample means?
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SECTION-B
11) a) Find the Karl Pearson's co-efficient of skewness from the following data :
Size :
1
2
3
4
5
6
7
Frequency : 10
18
30
25
12
3
2
b) From the following table, calculate the coefficient of correlation by karl Pearson's
method.
X
6
2
10
4
8
Y
9
11
?
8
7
Arithmetic means of X and Y series are 6 and 8 respectively.
12) a) Suppose that the time in minutes that a person has to wait at a certain station for a
train is found to be a random phenomenon with a probability function specified by the
distribution function :
0 ;
x 0
x
; 0 x 1
2
1
F (x)
;
1 x 2
2
x
;
2 x 4
4
1 ;
x 4
What is the conditional probability that the person will have to wait for a train
i) More than 3 minutes, given that it is more than 1 minutes.
ii) Less than www.FirstRanker.com
3 minutes, given that it is more than 1 minutes.
b) Two fair dice are thrown independently. Three events A, B and C is defined as
follows :
A : Even face with first dice
B : Even face with second dice
C : Sum of the points on the two dice is odd.
Discuss the independence of events A, B and C.
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13) a) Marks obtained by a number of students are assumed to be normally distributed with
mean 50 and variance 36. If four students are taken at random, what is the probability
2
that exactly two of them will have marks over 62? Given that
(z) dz 0.4772
0
where Z is N (0, 1).
b) If 2 percent of the books bound at a certain bindery have defective bindings.
Determine the probability that five of 400 books bound by this bindery will have
defective bindings.
14) a) Service calls come to a maintenance center, according to a Poisson process and, on
the average, 2.7 calls come per minute. Find the probability that (i) no more than 4
calls come in any minute, (ii) fewer than 2 calls came in any minute; (iii) more than
10 calls come in a 5-minute period.
b) If the two lines of regression are 4x ? 5y + 30 = 0 & 20x ? 9y ? 107 = 0. Which of
these is the line of regression of x on y, and y on x. Find correlation coefficients and
variance of Y when variance of X is 3.
SECTION-C
15) A continuous random variable X follows the probability law f (x) = Ax2, 0 x 1.
Determine A and find the probability that (i) X lies between 0.2 and 0.5 (ii) X is less than
1
1
3
1
0.3 (iii)
< X <
(iv) X >
given that X >
.
4
2
4
2
16) a) The length of time a person speaks over phone follows an exponential distribution
with mean 6. What is the probability that the person will talk for (i) more than 8
minutes and (ii) between 4 and 8 minutes?
b) A continuous random variable X has a probability density function f (x) = k (1 + x),
2 x 5. Find P(X 4).
17) a) Fit a second degree parabola to the following data :
X :
1
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2
3
4
5
Y :
1090
1220 1390
1625
1915
b) A reading test is given to an elementary school class that consists of 12 Anglo-
American children and 10 Mexico-American children. The results of test are :
Anglo American
Mexico American
Mean
74
70
Std.
8
10
Is the difference between means of the two groups significantly at the 0.05 level of
significance? Value of t at 5% level for 20 degree is freedom is 2.086.
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18) a) Before an increase in excise duty on tea, 400 people out of a sample of 500 persons
were found to be tea drinkers. After an increase in duty, 400 people were tea drinkers
in a sample of 600 people. Using standard error of proportion, state whether there is
significant decrease in the consumption of tea at 5% level of significance. Take value
of Z at 5% level of significance is 1.645.
b) The following table gives for a sample of married women, the level of education and
marriage adjustment score :
Marriage adjustment score
Very low
Low
High
Very High
College
24
97
62
58
Level of
High School
22
28
30
41
Education
Middle school
32
10
11
20
Can you conclude from the above, the higher the level of education, the greater is the
degree of adjustment in marriage? Use table value of chi-square at 5% level for 6d.f. =
12.59.
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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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This post was last modified on 04 November 2019