Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2142505 Probability And Introduction To Statistics Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2142505 Date: 13/12/2019
Subject Name: Probability and Introduction to Statistics
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Define/ explain following:
1. Random Experiment
2. Primary data
3. Ogives
03
(b) Calculate the mean for the following data
Class 0-7 7-14 14-21 21-28 28-35 35-42 42-49
Frequency 19 25 36 72 51 43 28
04
(c) Find variance, standard deviation and coefficient of variation for the following
data set.
Gross profit (in % of Sales 0-10 10-20 20-30 30-40 40-50
No. of Companies 22 38 46 35 20
07
Q.2 (a) Define/ explain following:
1. Random Variable
2. Cumulative Distribution Function
3. Compound Events
03
(b) Compare various measures of Central Tendencies. 04
(c) Discuss Joint Probability Distribution with suitable example. 07
OR
(c) Discuss Normal Distribution with suitable example. 07
Q.3 (a) State Baye?s Theorem 03
(b) Discuss Type-I and Type ?II error. 04
(c) When a machine is set correctly, it produces 25% defectives; otherwise it
produces 60% defectives. From the past knowledge and experience, the
manufacturer knows that the chances that the machine is set correctly or
wrongly are 50:50. The machine was set and before commencement of
production, one piece was inspected and found to be defectives. What is the
probability of machine set up being correct?
07
OR
Q.3 (a) Briefly explain Binomial Distribution 03
(b) Explain probability sampling method 04
(c) What is Probability? Discuss Classical approach and Bayesian Approach for
assigning probability.
07
Q.4 (a) Give properties of Expectation 03
(b) A machine produces 50 articles per day. On average 3 articles produced are
found defective in a day. If a sample of 15 articles are drawn at random, what
is the probability that one article of this lot is defective?
04
(c) Explain z-test with suitable example. 07
OR
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2142505 Date: 13/12/2019
Subject Name: Probability and Introduction to Statistics
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Define/ explain following:
1. Random Experiment
2. Primary data
3. Ogives
03
(b) Calculate the mean for the following data
Class 0-7 7-14 14-21 21-28 28-35 35-42 42-49
Frequency 19 25 36 72 51 43 28
04
(c) Find variance, standard deviation and coefficient of variation for the following
data set.
Gross profit (in % of Sales 0-10 10-20 20-30 30-40 40-50
No. of Companies 22 38 46 35 20
07
Q.2 (a) Define/ explain following:
1. Random Variable
2. Cumulative Distribution Function
3. Compound Events
03
(b) Compare various measures of Central Tendencies. 04
(c) Discuss Joint Probability Distribution with suitable example. 07
OR
(c) Discuss Normal Distribution with suitable example. 07
Q.3 (a) State Baye?s Theorem 03
(b) Discuss Type-I and Type ?II error. 04
(c) When a machine is set correctly, it produces 25% defectives; otherwise it
produces 60% defectives. From the past knowledge and experience, the
manufacturer knows that the chances that the machine is set correctly or
wrongly are 50:50. The machine was set and before commencement of
production, one piece was inspected and found to be defectives. What is the
probability of machine set up being correct?
07
OR
Q.3 (a) Briefly explain Binomial Distribution 03
(b) Explain probability sampling method 04
(c) What is Probability? Discuss Classical approach and Bayesian Approach for
assigning probability.
07
Q.4 (a) Give properties of Expectation 03
(b) A machine produces 50 articles per day. On average 3 articles produced are
found defective in a day. If a sample of 15 articles are drawn at random, what
is the probability that one article of this lot is defective?
04
(c) Explain z-test with suitable example. 07
OR
2
Q.4 (a) What is Simple Linear Regression? 03
(b) Let X and Y be the random variables such that E[X] = 2.8, E[Y] = 5.3, V[X]
= 18.6, V[Y] = 41.3. Compute the following:
1. E(X+1)
2. E(X+2Y+1)
3. V(2X+5)
4. V(6Y+9)
04
(c) For the probability distribution:
X 0 1 2 3 4
P(X) 0.25 0.35 0.25 0.10 0.05
Find E[X] and V[X]
07
Q.5 (a) Give properties of Binomial Distribution 03
(b) Explain application of Chi-Square Test 04
(c) Discuss F-test with suitable example. 07
OR
Q.5 (a) Explain Correlation Coefficient. 03
(b) Discuss Simple Random Sampling. 04
(c) Discuss ANOVA with suitable example. 07
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This post was last modified on 20 February 2020