# Data Science for Engineers | Week 3

### Session: JULY-DEC 2023

Course Name: Data Science for Engineers

#### 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).

Q1. Find the value of P(X>2.5|X<5). (Enter the answer correct to 2 decimal places).

Q2. Find the expected value of X.

#### These are NPTEL Data Science for Engineers Assignment 3 Answers

Q3. 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

Q4. A pharmaceutical company is testing a new drug. The probability that a patient experiencing a side effect from this drug is 0.10. If the drug is given to 5 patients, what is the probability that more than 1 patient will experience the side effect? (Enter the answer correct to 2decimal places.)

#### These are NPTEL Data Science for Engineers Assignment 3 Answers

Q5. Suppose X∼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≠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.

Answer: Accept H0 at a significance level of 0.10.

Q6. 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

#### These are NPTEL Data Science for Engineers Assignment 3 Answers

Q7. The correlation coefficient of two random variable X and Y is −14, their variance is given by 3 and 5. Compute Cov(X,Y).
-0.854
0.561
-0.968
None of the above

Q8. 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

Answer: Chi-square with N−1 degrees of freedom

#### These are NPTEL Data Science for Engineers Assignment 3 Answers

Q9. 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
0.0275
0.018

Q10. 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

#### These are NPTEL Data Science for Engineers Assignment 3 Answers

Course Name: Data Science for Engineers

#### Q1. 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).a. 5b. 8c. 33d. None of the above

Q2. 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

a. Accept H0
b. Reject H0

These are NPTEL Data Science for Engineers Assignment 3 Answers

Q3. 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)
a. 1.25
b. 5

Q4. Suppose X∼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≠10.5)?
a. Accept H0 at a significance level of 0.10.
b. Reject H0 at a significance level of 0.10.
c. Accept H0 at a significance level of 0.05.
d. Reject H0 at a significance level of 0.05.

Answer: d. Reject H0 at a significance level of 0.05.

These are NPTEL Data Science for Engineers Assignment 3 Answers

Q5. 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

Q6. 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

Answer: d. None of the above

These are NPTEL Data Science for Engineers Assignment 3 Answers

Q7. 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

Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows
a. Normal distribution
b. Chi-square with N degrees of freedom
c. Chi-square with N−1 degrees of freedom
d. t-distribution with N−1 degrees of freedom

Answer: c. Chi-square with N−1 degrees of freedom

These are NPTEL Data Science for Engineers Assignment 3 Answers

Q9. 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?
a. 0.0455
b. 0.455
c. 0.0275
d. 0.018

These are NPTEL Data Science for Engineers Assignment 3 Answers

Q10. Which one of the following is best measure of central tendency for categorical data?
a. Mean
b. Median
c. Mode
d. None of the above