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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
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Subject Code : BTAM-204-18
M.Code : 76257
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
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- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION - B & C have FOUR questions each.
- Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
- Select atleast TWO questions from SECTION - B & C.
SECTION-A
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Answer the following :
- Define Probability of an event.
- 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.
- What is Spearman’s rank correlation coefficient?
- State chi-square and Student’s t distributions.
- Define Discrete Variables.
- If arithmetic mean is 56.50, median is 59.50 and standard deviation is 12.40. Find the skewness.
- Differentiate between the discrete and continuous random variables.
- Write the normal equations for the curve fitting y = a + b x by the method of least squares.
- Define Regression Coefficients.
- Define Null and alternative hypothesis.
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SECTION-B
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a) Find the Karl Pearson's coefficient of skewness from the following data :
Size : 1 2 3 4 5 6
Frequency : 10 18 30 25 12 3 2
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b) Show that the correlation coefficient rxy between the two variables x and y is given by
rxy= (s2x +s2y -s2x-y) / 2sxsy
where sx, sy and sx-y are the standard deviations of x, y and x — y respectively.
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a) Two fair dice are thrown independently. Three events A, B and C is defined as follows :
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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.
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a) With the usual notations, find p for a binomial random variable X if n = 6 and 9P(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<Z< 1.75) = 0.46, where Z is standard normal variate.
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From the given data, find :
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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
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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SECTION-C
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The intelligence quotients (IQ) of 16 students from B.Tech. IInd 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.
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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.
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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?
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The prices of a commodity during 2011-2016 are given below. Fit a parabola Y =a+bX + cX2 to these data.
Year (X) | 2011 | 2012 | 2013 | 2014 | 2015 | 2016
Price (Rs.) (Y) | 100 | 107 | 128 | 140 | 181 | 192
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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 :
2 8 2 2 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 x2 for 9 d.f. at 5% level of significance is 16.919).
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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 download link is referred from the post: PTU B.Tech Question Papers 2020 March (All Branches)