Download SGBAU BSc 2019 Summer 2nd Sem Statistics Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) BSc 2019 Summer (Bachelor of Science) 2nd Sem Statistics Previous Question Paper

AW?1667
B.Sc. (Part?I) Semester?II Examination
STATISTICS
Time 2 Three Hours] [Maximum Marks : 80
1.
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YBC
Note :? All Questions are compulsory.
(A) Fill in the blanks :
(1) Karl Pearson?s coef?cient of correlation is also called as _ _ correlation coef?cient.
(ii) The point of intersection of two lines of regression is
(iii) Mean, mode and median ofthc normal distribution are
(iv) In Poisson distribution mean and variance arc _ 7 7 2
(B) C hoose the correct altemative :
(i) For perfect ncgative correlation r ? _.
(a) +1 (b) ?1
(C) 0 (d) 00
(ii') The term regression was ?rst studied by :
(3) Karl Pearson (b) Bemoulli
(c) Sir Francis Gallon ((1) RA. Fisher
(iii) The _ distribution is said to have a property of lack of memory.
(a) Binomial (b) Poisson
(c) Exponential (d) Negative binomial
(iv) For normal distribution [52 '? _ .
(a) 3 (b) *3
(c) 0 (d) 1 2
(C ) Answer the following questions in one sentence each :
(i) What do you mean by dichotomous clzmsi?cation ?3
(ii) What is a correlation coef?cient ?3
(iii) State the continuous distribution for which mean is equal to variance.
(iv) What do you mean by standard normal variate ? 4
(A) Show that coef?cient ofcorrclation lies between 1 and + 1. 4
(B) Dcrivc the formula for Spcarrnan?s rank correlation coef?cient. 4
(C) Dc?nc intraclass correlation with example. 4
OR
(1?) Describe the Scatter diagram. 4
(Q) Show that Karl Pearson?s coef?cient of correlation is independent of change oforigin and
scale. 4
(R) De?ne and state the formula for Kendall?s rank correlation. 4
1524mm l (Contd.)

4. (A)
(B)
(C)
5. (P)
(Q)
(R)
6. (A)
(B)
(C)
7. (P)
(Q)
(R)
8. (A')
(B)
? (Q)
10. (A)
(B)
(C)
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What do you mean hy rcgrcsshm 4
Obtain the normal equations 1b! ?tting a simighl line. 4
Explain the term mult'ple correlation with the help ul?cxamplc. 4
OR
De?ne the two regression cuc?icicms. Prove any one property 01' regression cocf?cient.4
Derive the equation 01' line nt? regression of Y on X 4
Obtain the nomlal equations I'm titling an exponential curw. 4
Explain the term consistency 01? daza. Obtain the conditiun of consistency in case of two
attributes A and B. 4
Explain independence ul?am'ilmlcs. State Ihc criteria for independence ofthe atTrihutes
A and B. 4
Examine the consistency of givm dulu N ? IUOO. (A) ? 600. (B) ? 500. (AB) ? 50.
4
OR
De?ne the following tcnns :
(i) Ultimile classes
(ii) Association oi?atlribulm
(iii) Ordcr ofclasscs and 0.11? lrcqucnciw
(\iv) Pmitive clzms and negmiw :luss. 4
Give the criteria for consis?cm} ol' [\u) attributes A. B and C. 4
Den've the [elationship between Yuiek coef?cient of masociation (Q) and coe?icient Ofcolligation
(Y) 4
State the probability mzm Function of Binomial distribution and obtain its cumulant generating
function. 6
Obtain main and variance L 1? Llimsrcic unifumx distribution. 6
()R
Derive the recurrence rclatinn [01? the moments of Binomial distribution. 6
Obtain the mgfof negative binomial distribution and hence ?nd its mean and variance. 6
Obtain the moment generating I?uncLion of Poisson distribution. 4
Obtain mean and variance ul'hypcrgcomclric distribution. 4
De?ne geometric distribution. Ohtuin its mgf and hence ?nd mean and variance. 4
()R
7
(Contd.)

11. (P) Show that Poisson distribution is a limiting case of Binomial distribution. 4
(Q) Show that mean and variance 01? 1116 geometric distribution
p(x) : q?p X ? 0.1.2. .....
are respectively qp ?, qp?z. 4
(R) De?ne Hypergeometric distributioh and show that it tends to Binomial distribution under
certain condition. 4
12. (A) State the pdf of continuous unifonn distribution and obtain its mgf. 6
(B) State the pdf of normal distribution and obtain its mode. 6
OR
13. (P) State the pdt?ot?univariatc gamma distribution and obtain its mean and variance. 6
(Q) State any four chief characteristics of normal distribution. 6
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b)
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