ABOUT THE COURSE :

Learning Objectives :

Introduce R as a programming language
Introduce the mathematical foundations required for data science
Introduce the first level data science algorithms
Introduce a data analytics problem solving framework
Introduce a practical capstone case study

Learning Outcomes:

Describe a flow process for data science problems (Remembering)
Classify data science problems into standard typology (Comprehension)
Develop R codes for data science solutions (Application)
Correlate results to the solution approach followed (Analysis)
Assess the solution approach (Evaluation)
Construct use cases to validate approach and identify modifications required (Creating)

INTENDED AUDIENCE: Any interested learner

PREREQUISITES: 10 hrs of pre-course material will be provided, learners need to practise this to be ready to take the course.

INDUSTRY SUPPORT: HONEYWELL, ABB, FORD, GYAN DATA PVT. LTD.

NPTEL Data Science for Engineers Week 3 Assignment Answer

Course layout

Week 1: Course philosophy and introduction to R

Week 2: Linear algebra for data science

1. Algebraic view – vectors, matrices, product of matrix & vector, rank, null space, solution of over-determined set of equations and pseudo-inverse)
2. Geometric view – vectors, distance, projections, eigenvalue decomposition

Week 3: Statistics (descriptive statistics, notion of probability, distributions, mean, variance, covariance, covariance matrix, understanding univariate and multivariate normal distributions, introduction to hypothesis testing, confidence interval for estimates)

Week 4: Optimization

Week 5: 1. Optimization

2. Typology of data science problems and a solution framework

Week 6: 1. Simple linear regression and verifying assumptions used in linear regression

2. Multivariate linear regression, model assessment, assessing importance of different variables, subset selection

Week 7: Classification using logistic regression

Week 8: Classification using kNN and k-means clustering

NPTEL Data Science for Engineers Week 3 Assignment Answer

Week 3 : Assignment 3

Due date: 2025-02-12, 23:59 IST.

Assignment not submitted

1 point

Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an odd number. He selects an odd number randomly. If the random variable $X$ denotes the last digit of the contact number, then calculate Var( $X$ ).

None of the above

1 point

Suppose $X \sim Normal (µ, 4)$ . For $n$ = 20 iid samples of $X$ , the observed sample mean is 5.2. What conclusion would a z-test reach if the null hypothesis assumes $µ$ = 5 (against an alternative hypothesis $µ \neq$ 5) at a significance level of $α$ = 0.05?
Use $F_{z}^{- 1}$ (0.025) = −1.9599

Accept $H_{0}$

Reject $H_{0}$

1 point

A box contains 8 items out of which 2 are defective. A sample of 5 items is to be selected randomly (without replacement) from the box. If the random variable $X$ represents the number of defective items in a selection of 5 items, then find $E (X)$ .(Enter the answer correct to 2 decimal places)

1.25

0.4

1.3

1 point

Suppose $X \sim Normal (µ, 9)$ . For n = 100 iid samples of $X$ , the observed sample mean is 11.8. What conclusion would a z-test reach if the null hypothesis assumes $µ = 10.5$ (against an alternative hypothesis $µ \neq 10.5$ )?

Accept $H_{0}$ at a significance level of 0.10.

Reject $H_{0}$ at a significance level of 0.10.

Accept $H_{0}$ at a significance level of 0.05.

Reject $H_{0}$ at a significance level of 0.05.

1 point

Let $X$ and $Y$ be two independent random variables with Var( $X$ ) = 9 and Var( $Y$ ) = 3, find Var( $4 X - 2 Y + 6$ ).

100

140

156

None of the above

1 point

The covariance between two random variable $X$ and $Y$ is −3.749, their variance is given by 3 and 5. Compute the correlation coefficient.

-0.854

0.561

-0.968

None of the above

1 point

When will you reject the Null hypothesis?

$p$ value greater than $α$

$p$ value less than $α$

$p$ value equal to $α$

None of the above

1 point

A sample of $N$ observations are independently drawn from a normal distribution. The sample variance follows

Normal distribution

Chi-square with $N$ degrees of freedom

Chi-square with $N$ − 1 degrees of freedom

t-distribution with $N$ − 1 degrees of freedom

1 point

A car manufacturer purchases car batteries from two different suppliers. Supplier $X$ provides 55% of the batteries and supplier Y provides the rest. 5% of all batteries from supplier $X$ are defective and 4% of all batteries from supplier $Y$ are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier $X$ ?

0.0455

0.455

0.604

0.018

1 point

Which one of the following is best measure of central tendency for categorical data?

Mean

Median

Mode

None of the above

NPTEL Data Science for Engineers Week 3 Assignment Answer

NPTEL Data Science for Engineers Week 3 Assignment Answer

Course layout

NPTEL Data Science for Engineers Week 3 Assignment Answer

Week 3 : Assignment 3

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