Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 4th Sem New 2142505 Probability And Introduction To Statistics Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER?IV(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2142505 Date:17/05/2019
Subject Name: Probability and Introduction to Statistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Explain in brief: What is operation research? 03
(b) Define: (i) Range (ii) Quartile deviation (iii) Average deviation (iv)Variance. 04
(c) Explain different types of graphs (charts) which are used to present statistical data. 07
Q.2 (a) What is data? List various types of data and explain any one of them. 03
(b) Compare various measures of central tendencies. 04
(c) Calculate the mode using analytical and graphical method for the following
distribution.
Gross profit
as percentage
of sales
0-7 7-14 14-21 21-28 28-35 35-42 42-49
Number of
companies
19 25 36 72 51 43 28
07
OR
(c) In a survey of 50 chemical industries the following data was collected: Calculate the
variance for the distribution.
Level of
profit
10 15 20 25 30
Number of
companies
15 10 15 6 4
07
Q.3 (a) Explain Skewness and Kurtosis. 03
(b) Explain the basic rules for probability. 04
(c) Describe conditional probability with suitable example. 07
OR
Q.3 (a) Discuss the properties of Hyper Geometric Distribution. 03
(b) Explain Chi-Square '' test for goodness of fit''. 04
(c) Explain Analysis of Variance (ANOVA).
07
Q.4 (a) Define : (i) Null Hypothesis (ii) Systematic Sampling (iii) Mode 03
(b) What is Simple Linear Regression? 04
(c) An item is manufacture by three machines, M1, M2, M3. Out of the total
manufacturing during specified production period, 50% are manufactured on M1,
30% on M2, and 20% on M3.it is also known that 2% of item are produced by M1
and M2 are defective, While 3% of those manufacture on M3 are defective. All items
are put into on bin. From the bin , One item is drawn random and found to be defective.
What is the probability that it was made on M1, M2, M3???
07
OR
Q.4 (a) Define : (i) Event (ii) Ogives (iii) Geometric mean 03
(b) What are Null Hypothesis and Alternate Hypothesis? 04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER?IV(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2142505 Date:17/05/2019
Subject Name: Probability and Introduction to Statistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Explain in brief: What is operation research? 03
(b) Define: (i) Range (ii) Quartile deviation (iii) Average deviation (iv)Variance. 04
(c) Explain different types of graphs (charts) which are used to present statistical data. 07
Q.2 (a) What is data? List various types of data and explain any one of them. 03
(b) Compare various measures of central tendencies. 04
(c) Calculate the mode using analytical and graphical method for the following
distribution.
Gross profit
as percentage
of sales
0-7 7-14 14-21 21-28 28-35 35-42 42-49
Number of
companies
19 25 36 72 51 43 28
07
OR
(c) In a survey of 50 chemical industries the following data was collected: Calculate the
variance for the distribution.
Level of
profit
10 15 20 25 30
Number of
companies
15 10 15 6 4
07
Q.3 (a) Explain Skewness and Kurtosis. 03
(b) Explain the basic rules for probability. 04
(c) Describe conditional probability with suitable example. 07
OR
Q.3 (a) Discuss the properties of Hyper Geometric Distribution. 03
(b) Explain Chi-Square '' test for goodness of fit''. 04
(c) Explain Analysis of Variance (ANOVA).
07
Q.4 (a) Define : (i) Null Hypothesis (ii) Systematic Sampling (iii) Mode 03
(b) What is Simple Linear Regression? 04
(c) An item is manufacture by three machines, M1, M2, M3. Out of the total
manufacturing during specified production period, 50% are manufactured on M1,
30% on M2, and 20% on M3.it is also known that 2% of item are produced by M1
and M2 are defective, While 3% of those manufacture on M3 are defective. All items
are put into on bin. From the bin , One item is drawn random and found to be defective.
What is the probability that it was made on M1, M2, M3???
07
OR
Q.4 (a) Define : (i) Event (ii) Ogives (iii) Geometric mean 03
(b) What are Null Hypothesis and Alternate Hypothesis? 04
2
(c) Discuss t-test with suitable example. 07
Q.5 (a) Explain correlation coefficient. 03
(b) Suppose a random variable X has the following probability function:
X 4 6 8 10
P(X) 0.2 0.3 0.4 0.5
Find expectation and variance of X.
04
(c) Explain Normal distribution with suitable example. 07
OR
Q.5 (a)
(b)
(c)
Find the Harmonic mean of 4, 8, 16, 32, 64.
A random variable X has a Poisson distribution with a mean of 3. Find P (1 ? X ? 3)?
Explain briefly scatter diagram with suitable example.
03
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This post was last modified on 20 February 2020