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Question Bank UT II

The document is a question bank for an Internal Assessment Test covering statistical techniques, probability, and Fourier series. It includes various problems such as calculating Spearman’s rank correlation, fitting parabolic curves, finding regression coefficients, and working with probability distributions. Each question is assigned a specific mark value, indicating its weight in the assessment.

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shashank gawade
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9 views1 page

Question Bank UT II

The document is a question bank for an Internal Assessment Test covering statistical techniques, probability, and Fourier series. It includes various problems such as calculating Spearman’s rank correlation, fitting parabolic curves, finding regression coefficients, and working with probability distributions. Each question is assigned a specific mark value, indicating its weight in the assessment.

Uploaded by

shashank gawade
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Question Bank

Internal Assessment Test II

Module 5: Statistical Technique (CO 5)


Q.1 Calculate Spearman’s rank correlation coefficient R (06 M)
X 10 12 18 18 15 40
Y 12 18 25 25 50 25

Q.2 Fit a second-degree parabolic curve to the following data (06 M)


Year(X) 1974 1975 1976 1977 1978 1979 1980 1981
Production(Y) 12 14 26 42 40 50 52 53

Q.3 Consider the equations of regression lines 5𝑥 − 𝑦 = 22,64𝑥 − 45𝑦 = 24 . Find


̅ 𝑦̅ and correlation coefficient r
𝑥, (06 M)
Q.4 Find the coefficients of regression and hence obtain the equation of the lines of
regression for the following data (08 M)
X 78 36 98 25 75 82 90 62 65 39
Y 84 51 91 60 68 62 86 58 53 47

Module 6 : Probability (CO 6)


Q.1 Two unbiased dice are thrown.If X represents sum of the numbers on the two dice.
Write Probability distribution of the random variable X and find mean, standard
deviation (06 M)
Q.2 A continuous random variable has probability density function (06 M)

𝑘 (𝑥 − 𝑥 2 ) , 0 ≤ 𝑥 ≤ 1
𝑓(𝑥 ) = {
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Find k , mean and variance
Q.3 The probability density function of a random variable X is (08 M)

X 0 1 2 3 4 5 6
P(X=x) k 3k 5k 7k 9k 11k 13k
Find k , P(X<4) , P(3<X≤6) , mean , variance and standard deviation of X.

Module 3 : Fourier Series (CO 3)

Q.1 Find a fourier series represents 𝑓 (𝑥 ) = 𝑥 2 in (0,2π) (06 M)

Q.2 Obtain a fourier series represents 𝑓 (𝑥 ) = 𝑥 3 in (-π,π) (06 M)

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