Statistical Methods

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The Statistical Methods for Economics Course for BA (Hons) Economics Semester III, Delhi University has been taught by Mr. Dheeraj Suri. The Video Lectures are based upon the books prescribed by the University of Delhi. The Duration of Video Lectures is approximately 50 Hours.

Course Fee : Rs. 7,000

Access of Video Lectures is provided on one device, Windows Computer or Android Phone, till end of Semester III Exams.

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  • Full Course Video Lectures
  • Complete Study Material (PDF Notes) which includes Concepts, Previous Year Questions, Numerical Questions, MCQ’s and Important Questions
  • Online Discussion Forum to Post Your Queries to Discuss with Faculty & other fellow Students
  • Live online Doubts Sessions (at least twice a week) for resolution of Doubts
  • Mock Tests at the Website
  • Video Lectures Cover Theory Portions Exchaustively + Complete Solutions of Back Questions of readings + Solutions of Previous Years Papers + Large Number of Numericals

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Access of Video Lectures is provided on one device, Windows Computer or Android Phone, till end of the Semester II Exams

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Demo Lectures

SME, Course Introduction

Demo PDF of Study Material

Chapter-4-Probability

Demo Quiz

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Probability Test #5

1. Please Read the Questions and all the options Carefully, Before Selecting Your Choice.
2. You are not Allowed to edit your answers after submission.
3. The Paper has ten Questions
4. Time Allowed is 10 Minutes.
5. It is necessary to enter your valid Email id to attempt this test.

 

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1 / 10

Two patients share a hospital room for two days. Suppose that, on any given day, a person independently picks up an airborne infection with probability 1/4. An individual who is infected on the first day will certainly pass it to the other patient on the second day. Once contracted, the infection stays for at least two days. What is the probability that fewer than two patients have the infection by the end of the second day? 

2 / 10

Suppose 1/10 of the population has a disease. If a person has the disease, then a test detects it with probability 8/10. If a person does not have the disease, then the test incorrectly shows the presence of the disease with probability 2/10. What is the probability that the person tested has the disease if the test indicates the presence of the disease?

3 / 10

There are 3 red and 5 black balls in an urn. You draw two balls in succession without replacing the first ball.
The probability that the second ball is red equals

4 / 10

An insurance policy-holder can submit up to 5 claims. The probability that the policyholder submits exactly n claims is pn, for n = 0, 1, 2, 3, 4, 5. It is known that
(a)  The difference between pn and pn + 1 is constant for n = 0, 1, 2, 3, 4, and 

(b)  40% of the policyholders submit 0 or 1 claim.
What is the probability that a policy-holder submits 4 or 5 claims?

5 / 10

A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 to that tourist. The expected revenue of the tour operator is 

6 / 10

In a roll of two fair dice, X is the number on first die and Y is the number on second die. Which of the following statements is True

7 / 10

A family has two children, what is the probability that both are girls given that at least one child is girl?

8 / 10

A student is answering a multiple‐choice examination. Suppose a question has m possible answers. The student knows the correct answer with probability p. If the student knows the correct answer, then she picks that answer; otherwise, she picks randomly from the choices with probability 1/m each. Given that the student picked the correct answer, the probability that she knew the correct  answer is

9 / 10

Suppose two fair dice are tossed simultaneously. What is the probability that the total number of spots on the upper faces of the two dice is not divisible by 2, 3, or 5?

10 / 10

A coin toss has possible outcomes H and T with probabilities 3/4 and 1/4 respectively. A gambler observes a sequence of tosses of this coin until H occurs. Let the first H occur on the nth toss. If n is odd, then the gambler’s prize is −2n , and if n is even, then the gambler’s prize is 2n . What is the expected value of the gambler’s prize?

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Exam Pattern

Assessment :

This course carries 100 marks of which the end semester examination is 75 marks and internal assessment is worth 25 marks as per the following norms: Two class tests/assignment of 10 marks each and 5 marks for attendance.

The following distribution of topics and marks, and the amount of choice within each topic, was agreed upon:
a. Section 1: Unit 1 and Unit 2: (indicative weightage 10 marks), Two questions of 5 marks each with one question from Unit 1 and the other from Unit 2. No internal choice in these units should be given.
b. Section 2: Unit 3 and Unit 4: (indicative weightage 25 marks), One compulsory question of 5 marks and Two questions out of Three for 10 marks each.
c. Section 3: Unit 5: (indicative weightage 20 marks), Two questions out of Three for 10 marks each.
d. Section 4: Unit 6: (indicative weightage 20 marks), Two questions out of Three for 10 marks each.

Course Content of Our Video Lectures

Unit – I : Introduction & Overview

Chapter 1 : Introduction & Overview [60 Minutes]

Based Upon J L Devore Chapter 1.1

Number of Lectures   1 Lectures

Total Duration   60 Minutes

Number of Questions in Notes   10 Questions

Number of MCQ Tests on this Chapter   1 Tests

Important Topics Covered : Population & Sample

Unit – II : Elementary Probability Theory

Chapter 2 : Probability [542 Minutes]

Based Upon J L Devore Chapter 2

Number of Lectures   13 Lectures

Total Duration   542 Minutes

Number of Questions in Notes   376 Questions

Number of MCQ Tests on this Chapter   6 Tests

Important Topics Covered : Sample space, Events, Use of Combinations & Permutations, Addition Theorem, Conditional Probability, Independent Events & Multiplication Theorem, Bayes Theorem, Mathematical Expectation

Unit – III : Random Variables & Probability Distributions

Chapter 3 : Discrete Random Variables [521 Minutes]

Based Upon J L Devore Chapter 3

Number of Lectures   11 Lectures

Total Duration   521 Minutes

Number of Questions in Notes   229 Questions

Number of MCQ Tests on this Chapter   6 Tests

Important Topics Covered : Discrete Random Variable, PMF, CDF, Binomial Distribution, Hypergeometric Distribution, Poisson Distribution

Chapter 4 : Continuous Random Variables [337 Minutes]

Based Upon J L Devore Chapter 4

Number of Lectures   8 Lectures

Total Duration   337 Minutes

Number of Questions in Notes   102 Questions

Number of MCQ Tests on this Chapter   6 Tests

Important Topics Covered : Probability Density Function, CDF, Uniform Distribution, Normal Distribution, Exponential & Gamma Distribution

Unit – IV : Random Sampling & Jointly Distributed Random Variables

Chapter 5 : Joint Probability DIstributions [243 Minutes]

Based Upon J L Devore Chapter 5

Number of Lectures   5 Lectures

Total Duration   243 Minutes

Number of Questions in Notes   60 Questions

Number of MCQ Tests on this Chapter   4 Tests

Important Topics Covered : Joint PMF, Marginal PMF, Joint PDF, Marginal PDF, Conditional Distributions, Covariance, Correlation, Properties of Correlation, Statistics & their Distribution, Distribution of Sample Mean, Distribution of a Linear Combination

Unit – V : Point & Interval Estimation

Chapter 6 : Point Estimation [307 Minutes]

Based Upon J L Devore Chapter 6

Number of Lectures   7 Lectures

Total Duration   307 Minutes

Number of Questions in Notes   68 Questions

Number of MCQ Tests on this Chapter   5 Tests

Important Topics Covered : Sampling, Point Estimate, MVUE, Standard Error of an Estimator, MLE, Method of Moments, Central Limit Theorem

Chapter 7 : Confidence Intervals [230 Minutes]

Based Upon J L Devore Chapter 7

Number of Lectures   5 Lectures

Total Duration   230 Minutes

Number of Questions in Notes   73 Questions

Number of MCQ Tests on this Chapter   5 Tests

Important Topics Covered : Properties of a Confidence Interval, Confidence Interval of a Single Mean & Proportion, t & chi square distribution, Confidence Bounds

Unit – VI : Hypothesis Testing

Chapter 8 : Hypothesis Testing [212 Minutes]

Based Upon J L Devore Chapter 8

Number of Lectures   4 Lectures

Total Duration   212 Minutes

Number of Questions in Notes   66 Questions

Number of MCQ Tests on this Chapter   4 Tests

Important Topics Covered : Hypothesis Testing, Type I & Type II Errors, Power of a Test, P Values

Solutions of Previous Year Papers

2021 Paper

Duration of Lectures : 110 Minutes

2020 Paper

Duration of Lectures : 100 Minutes

2019 Paper

Duration of Lectures : 120 Minutes

2018 Paper

Duration of Lectures : 110 Minutes

End of Syllabus

Syllabus for SME as Prescribed by University of Delhi

Minutes-of-Meeting

Course Description

Statistical Methods for Economics (HC33)
Core Course (CC) Credit: 6

Course Objective
The course teaches students the basics of probability theory and statistical inference. It sets a necessary foundation for the econometrics courses within the Honours programme. The familiarity with probability theory will also be valuable for courses in advanced microeconomic theory.

Course Learning Outcomes
At the end of the course, the student should understand the concept of random variables and be familiar with some commonly used discrete and continuous distributions of random variables. They will be able to estimate population parameters based on random samples and test hypotheses about these parameters. An important
learning outcome of the course will be the capacity to analyse statistics in everyday life to distinguish systematic differences among populations from those that result from random sampling.

Unit 1
Introduction and overview The distinction between populations and samples and between population parameters and sample statistics

Unit 2
Elementary probability theory Sample spaces and events; probability axioms and properties; counting techniques; conditional probability and Bayes’ rule; independence

Unit 3
Random variables and probability distributions Defining random variables; probability distributions; expected values and functions of random variables; properties of commonly used discrete and continuous distributions (uniform, binomial, exponential, Poisson, hypergeometric and Normal random variables)

Unit 4
Random sampling and jointly distributed random variables Density and distribution functions for jointly distributed random variables; computing expected values of jointly distributed random variables; covariance and correlation coefficients

Unit 5
Point and interval estimation Estimation of population parameters using methods of moments and maximum likelihood procedures; properties of estimators; confidence intervals for population parameters

Unit 6
Hypothesis testing Defining statistical hypotheses; distributions of test statistics; testing hypotheses related to population parameters; Type I and Type II errors; power of a test; tests for comparing parameters from two samples

References

1. Devore, J. (2012). Probability and statistics for engineers, 8th ed. Cengage Learning.

2. Larsen, R., Marx, M. (2011). An introduction to mathematical statistics and its applications. Prentice Hall.

3. Miller, I., Miller, M. (2017). J. Freund’s mathematical statistics with applications, 8th ed. Pearson.