GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
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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
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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| MARKS | ||
| Q.1 | (a) Define/ explain following: | 03 |
| 1. Random Experiment | ||
| 2. Primary data | ||
| 3. Ogives | ||
| (b) Calculate the mean for the following data | 04 | |
| Class 0-7 | 7-14 | 14-21 | 21-28 | 28-35 | 35-42 | 42-49 | ||
| Frequency | 19 25 36 72 51 43 28 | ||
| (c) Find variance, standard deviation and coefficient of variation for the following data set. | 07 | |
| Gross profit (in % of Sales | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | ||
| No. of Companies 22 38 46 35 20 | ||
| Q.2 | (a) Define/ explain following: | 03 |
| 1. Random Variable | ||
| 2. Cumulative Distribution Function | ||
| 3. Compound Events | ||
| (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 | ||
| 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:
| 04 | |
| (c) For the probability distribution: --- Content provided by FirstRanker.com --- X 0 1 2 3 4P(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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