# NPTEL Data Science for Engineers Assignment 3 Answers 2023

NPTEL Data Science for Engineers Assignment 3 Answers 2023:- All the Answers provided below to help the students as a reference, You must submit your assignment at your own knowledge.

## NPTEL Data Science For Engineers Week 3 Assignment Answers 2023

A six sided die is marked ‘1’ on one face, ‘2’ on two of its faces, and ‘3’ on the remaining three faces. The die is thrown twice. Let X denotes the total score in two throws.
Based on the above information, answer questions (1), (2).

1. Find the value of P(X>2.5|X<5). (Enter the answer correct to 2 decimal places).

2. Find the expected value of X.

3. Suppose X ∼ 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≠5) at a significance level of α=0.05?
Use F−1z(0.025)=−1.9599

• Accept H0
• Reject H0

4. A pharmaceutical company is testing a new drug. The probability that a patient experiencing a side effect from this drug is 0.100.10. If the drug is given to 55 patients, what is the probability that more than 1 patient will experience the side effect? (Enter the answer correct to 22 decimal places.)

5. Suppose X∼Normal(μ,9)(μ,9). For n=100 iid samples of X, the observed sample mean is 11.811.8. What conclusion would a z-test reach if the null hypothesis assumes μ=10.5μ (against an alternative hypothesis μ≠10.5μ≠10.5)?

• Accept H0 at a significance level of 0.10.
• Reject H0 at a significance level of 0.10.
• Accept H0 at a significance level of 0.05.
• Reject H0 at a significance level of 0.05.

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

• 100
• 140
• 156
• None of the above

7. The correlation coefficient of two random variable X and Y is −14, their variance is given by 3and 5. Compute Cov(X,Y).

• -0.854
• 0.561
• -0.968
• None of the above

8. 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

9. A car manufacturer purchases car batteries from two different suppliers. Supplier X provides 55% of the batteries and supplier Y provides the rest. 5%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
• 0.0275
• 0.018

10. Find the t-statistic for the sample data, given that the population mean of the distribution is 8.

• -3.155
• 8.33
• -2.99
• None of the above

## NPTEL Data Science for Engineers Assignment 3 Answers 2022 [July 2022]

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

a. 100
b. 140
c. 156
d. None of the above

2. Calculate the standard error of sample mean using the following data n=14,μ=18.5,X¯=17.85,S=1.95n=14,μ=18.5,X¯=17.85,S=1.95

a. 0.52
b. 0.81
c. 0.23
d. None of the above

3. The correlation coefficient of two random variable X and Y is −14−14 , their variance is given by 3 and 5. Compute Cov(X,Y)Cov(X,Y)

a. -0.854
b. 0.561
c. -0.968
d. None of the above

4.Find the t-statistic for the sample data given that the population mean of the distribution is 8.

a. 3.93
b. 1.44
c. 8.33
d. None of the above

5.Find F-statistic for the following sample sets generated from the same distribution

a. 0.14
b. 1.47
c. 4.46
d. None of the above

6. Find the Fstatistic for the following sample sets generated from the distributions with population variances 3 and 7 respectively

a. 6.88
b. 0.73
c. 4.36
d. None of the above

7. When will you reject the Null hypothesis?

a. p value greater than α
b. p value less than α
c. p value equal to α
d. None of the above

8. A standard normal density function is shown below. The area of the shaded region is

a. 0.046
b. 0.977
c. 0.954
d. None of the above

9. A talent exam is conducted annually which has a mean score of 200 and a standard deviation of 30. If a student’s Z-score is 1.50, what was his score in the exam?

a. 245
b. 170
c. 230
d. None of the above

10. A car company purchases engine blocks from suppliers A, B, and C. Out of the 100 units supplied by A, two units were found to be defective. Similarly, out of 200 and 300 units supplied by B and C, the number units found to be defective were 10 and 15 respectively. If a quality control person of the car company picks up a block and if the selected block is from A, what is the probability that the block is defective?

a. 0.020
c. 0.35
c. 0.33
d. None of the above

## What is Data Science for Engineers?

Data Science for Engineers is a fun-filled course where Domain Certification helps learners to gain expertise in a specific Area/Domain. This can be helpful for learners who wish to work in a particular area as part of their job or research or for those appearing for some competitive exam or becoming job-ready or specialising in an area of study.  Every domain will comprise Core courses and Elective courses. Once a learner completes the requisite courses per the mentioned criteria, you will receive a Domain Certificate showcasing your scores and the domain of expertise.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of the average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF THE AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

## NPTEL Data Science for Engineers Assignment 3 Answers [Jan 2022]

Q1. If A and B are two events such that P(A∪B)=34,P(A∩B)=14,P(ˉA)=23,then P(ˉA|B) is

(A) 3/4
(B) 5/8
(C) 3/8
(D) None of the above

Q2. State whether the following statements are true or false.

I. The t distribution ranges from −∞ to ∞

II. The t distribution is symmetrical and has a mean zero

(A) I – True, II – True
(B) I – True, II – False
(C) I – False, II – False
(D) None of the above

Answer:- (A) I – True, II – True

Q3. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3, find Var(4X−2Y+6)

(A) 100
(B) 140
(C) 156
(D) None of the above

Q4. Calculate the standard error of sample mean using the following data

Q5. The correlation coefficient of two random variable X and Y is −14 , their variance is given by 3 and 5. Compute Cov(X,Y)

(A) -0.854
(B) 0.561
(C) -0.968
(D) None of the above

Q6. If X∼Bin(n,p), then the standard error of p is

Q7. A standard normal density function is shown below. The area of the shaded region is

(A) 0.046
(B) 0.977
(C) 0.954
(D) None of the above

Q8. The value of the correlation coefficient lies between:

(A) −∞ to ∞
(B) −1 to 1
(C) 0 to 1
(D) 0 to ∞

Q9. When will you reject the Null hypothesis?

(A) p value greater than α
(B) p value less than α
(C) p value equal to α
(D) None of the above

Answer:- (B) p value less than α

Disclaimer:- We do not claim 100% surety of solutions, these solutions are based on our sole expertise, and by using posting these answers we are simply looking to help students as a reference, so we urge do your assignment on your own.