Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 2nd Sem BTAM 204 18 Mathematics Ii Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 & Onwards)/(CE)/(ME) (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 TWO 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 TWO questions from SECTION - B & C.
SECTION-A
Answer the following :
1) Define Probability of an event.
2) Let X be the random variable such that P(X = ?2) = P (X = ?1), P(X = 2) = P(X=1) and
P(X>0) = P(X<0) = P(X = 0). Obtain the probability mass function of X.
3) What is Spearman?s rank correlation coefficient?
4) State chi-square and Student?s t- distributions.
5) Define Discrete Variables.
6) If arithmetic mean is 56.50, median is 59.50 and standard deviation is 12.40. Find the
skewness.
7) Differentiate between the discrete and continuous random variables.
8) Write the normal equations for the curve fitting y = a + b x by the method of least
squares.
9) Define Regression Coefficients.
10) Define Null and alternative hypothesis.
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Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 & Onwards)/(CE)/(ME) (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 TWO 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 TWO questions from SECTION - B & C.
SECTION-A
Answer the following :
1) Define Probability of an event.
2) Let X be the random variable such that P(X = ?2) = P (X = ?1), P(X = 2) = P(X=1) and
P(X>0) = P(X<0) = P(X = 0). Obtain the probability mass function of X.
3) What is Spearman?s rank correlation coefficient?
4) State chi-square and Student?s t- distributions.
5) Define Discrete Variables.
6) If arithmetic mean is 56.50, median is 59.50 and standard deviation is 12.40. Find the
skewness.
7) Differentiate between the discrete and continuous random variables.
8) Write the normal equations for the curve fitting y = a + b x by the method of least
squares.
9) Define Regression Coefficients.
10) Define Null and alternative hypothesis.
2 | M-76257 (S1)-2038
SECTION-B
11) a) Find the Karl Pearson's coefficient of skewness from the following data :
Size : 1 2 3 4 5 6 7
Frequency : 10 18 30 25 12 3 2
b) Show that the correlation coefficient r
xy
between the two variables x and y is given
by
2 2 2
?
?
2
x y x y
xy
x y
r
? ? ?
? ?
?
?
where ?
x
, ?
y
and ?
x?y
are the standard deviations of x, y and x ? y respectively.
12) a) 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.
b) From a bag containing 4 white and 6 red balls, three balls are drawn at random. If
each white ball drawn carries a reward of Rs. 4 and each red ball Rs. 6, find the
expected reward of the draw.
13) a) With the usual notations, find p for a binomial random variable X if n = 6 and
9 P(X = 4) = P(X = 2).
b) If the flowers on a truck are classified as A, B, and C according to a size-weight index
as: under 75, between 75 and 80, and above 80. Find approximately (assuming a
normal distribution) the mean and standard deviation of a lot in which A are 58%, B
are 38% and C are 4%. Given that P(0< Z< 0.20) = 0.08 and P(0
14) From the given data, find :
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
a) The two regression equations,
b) The coefficient of correlation between the marks in Mathematics & Statistics
c) The most likely marks in Statistics when the marks in Mathematics are 30.
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Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 & Onwards)/(CE)/(ME) (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 TWO 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 TWO questions from SECTION - B & C.
SECTION-A
Answer the following :
1) Define Probability of an event.
2) Let X be the random variable such that P(X = ?2) = P (X = ?1), P(X = 2) = P(X=1) and
P(X>0) = P(X<0) = P(X = 0). Obtain the probability mass function of X.
3) What is Spearman?s rank correlation coefficient?
4) State chi-square and Student?s t- distributions.
5) Define Discrete Variables.
6) If arithmetic mean is 56.50, median is 59.50 and standard deviation is 12.40. Find the
skewness.
7) Differentiate between the discrete and continuous random variables.
8) Write the normal equations for the curve fitting y = a + b x by the method of least
squares.
9) Define Regression Coefficients.
10) Define Null and alternative hypothesis.
2 | M-76257 (S1)-2038
SECTION-B
11) a) Find the Karl Pearson's coefficient of skewness from the following data :
Size : 1 2 3 4 5 6 7
Frequency : 10 18 30 25 12 3 2
b) Show that the correlation coefficient r
xy
between the two variables x and y is given
by
2 2 2
?
?
2
x y x y
xy
x y
r
? ? ?
? ?
?
?
where ?
x
, ?
y
and ?
x?y
are the standard deviations of x, y and x ? y respectively.
12) a) 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.
b) From a bag containing 4 white and 6 red balls, three balls are drawn at random. If
each white ball drawn carries a reward of Rs. 4 and each red ball Rs. 6, find the
expected reward of the draw.
13) a) With the usual notations, find p for a binomial random variable X if n = 6 and
9 P(X = 4) = P(X = 2).
b) If the flowers on a truck are classified as A, B, and C according to a size-weight index
as: under 75, between 75 and 80, and above 80. Find approximately (assuming a
normal distribution) the mean and standard deviation of a lot in which A are 58%, B
are 38% and C are 4%. Given that P(0< Z< 0.20) = 0.08 and P(0
14) From the given data, find :
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
a) The two regression equations,
b) The coefficient of correlation between the marks in Mathematics & Statistics
c) The most likely marks in Statistics when the marks in Mathematics are 30.
3 | M-76257 (S1)-2038
SECTION-C
15) The intelligence quotients (IQ) of 16 students from B.Tech. Ilnd year showed a mean of
107 and a standard deviation of 10, while the IQs of 14 students from B.Tech. 1st year
showed a mean of 112 and a standard deviation of 8. Is there a significant difference
between the IQs of the two groups at significance levels of 0.05? Given that critical value
at 28 degree of freedom with 5% level of significance is 2.05.
16) a) Suppose that the life length of the two bulbs B1 and B2 have distribution N(x; 40,36)
and N(x; 45, 9) respectively. If the bulb is to be used for 45-hour period, which bulb
is to be preferred? If it is to be used for 48-hour period, which bulb is to be preferred?
Given that P(Z<0.83)=0.7967, P(Z<1.33)=0.9082, P(Z<1.00) = 0.8143.
b) The time required to repair a machine is exponentially distributed with parameter ?.
What is the probability that a repair time exceeds 2 hours? What is the conditional
probability that a repair time takes at least 10 hours given that its duration exceeds 9
hours?
17) The prices of a commodity during 2011-2016 are given below. Fit a parabola
Y = a + bX + cX
2
to these data.
Year (X) 2011 2012 2013 2014 2015 2016
Price (Rs.) (Y) 100 107 128 140 181 192
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 peoples were tea drinker
in a sample of 600 people. Using standard error of proportion, state whether there is a
significant decrease in the consumption of tea. Take level of significance at 5%.
b) The number of scooter accidents per month in a certain town were as follows :
12 8 20 2 14 10 15 6 9 4
Are these frequencies in agreement with the belief that accident conditions were the same
during this 10 month period? (The table value of
2
? for 9 d.f. at 5% level of significance
is 16.919).
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 21 March 2020