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Question 221 MCQ · 1.0 marks
Latent demand in a demand-response curve is the area obtained when?
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Price is reduced below the identified optimal price
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Price is increased beyond the identified optimal price
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The optimal price is increased beyond the maximum available price
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Quantity is reduced below the identified optimal quantity
Published solution
**1. Interpret latent demand:** At the chosen price, some potential buyers do not purchase. Reducing price below that level makes additional buyers willing to buy, revealing demand that was latent at the original price.
**Answer: A — Price is reduced below the identified optimal price.**
A: **Correct:** A lower price reveals additional willingness to purchase below the chosen price.
B: **Incorrect:** Raising price removes buyers rather than revealing additional lower-price demand.
C: **Incorrect:** A price beyond the choke price produces no positive linear-model demand.
D: **Incorrect:** Reducing quantity alone does not describe the lower-price latent-demand area.
Which of the following distributions is/are Symmetric in nature (choose all that are applicable)?
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Standard Normal distribution
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Standard Binomial distribution
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Uniform distribution
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Poisson distribution
Published solution
**1. Identify symmetric families:** The standard normal is symmetric about zero; a continuous Uniform(a,b) is symmetric about (a+b)/2.
**2. State the binomial condition:** Binomial(n,p) is symmetric when p=1/2. A finite-mean Poisson is generally right-skewed, although its shape becomes approximately symmetric for large λ.
**Answer: A, B, C — A, B and C, with B requiring p=1/2.**
**Convention note:** “Standard Binomial” is not a universally defined distribution. If it means an arbitrary binomial rather than p=1/2, only A and C are necessarily symmetric.
A: **Correct:** The standard normal density is symmetric about 0.
B: **Correct:** Correct under the intended standard-binomial convention p=1/2.
C: **Correct:** A continuous uniform density on an interval is symmetric about its midpoint.
D: **Incorrect:** Its skewness is 1/√λ>0 for finite positive λ.
**(The following is a purely imaginary scenario)**
An insurance company believes that people can be divided into two classes: “Class-1: Those who are
accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that
an accident-prone person will have an accident at sometime within a fixed 1-year period with
probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It
is assumed that 30 percent of the human population is accident prone. Given this information,
answer the sub-questions.
What is the probability that a new policyholder will have an accident within a year of purchasing a
policy? (Note: Enter the answer **rounded to two decimal places**. For example, if the answer is “1.235”,
**then enter it as “1.24”**)
Published solution
**1. Partition policyholders:** Accident-prone people have probability 0.30 and others 0.70.
**2. Apply total probability:** \(P(A)=0.30(0.40)+0.70(0.20)=0.12+0.14=0.26\).
**Answer: 0.26.**
**(The following is a purely imaginary scenario)**
An insurance company believes that people can be divided into two classes: “Class-1: Those who are
accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that
an accident-prone person will have an accident at sometime within a fixed 1-year period with
probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It
is assumed that 30 percent of the human population is accident prone. Given this information,
answer the sub-questions.
Suppose you learn that a new policyholder has an accident within a year of purchasing a policy.
Then, what is the probability that the person is accident prone? (Note: Enter the answer **rounded to**
**two decimal places**. For example, if the answer is “1.235”, **then enter it as “1.24”)**
Published solution
**1. Compute the relevant probabilities:** \(P(\text{prone},A)=0.30(0.40)=0.12\), and \(P(A)=0.12+0.70(0.20)=0.26\).
**2. Use Bayes’ rule:** \(P(\text{prone}\mid A)=0.12/0.26\approx0.461538\), rounding to 0.46.
**Answer: 0.46.**
**(The following is a purely imaginary scenario)**
An insurance company believes that people can be divided into two classes: “Class-1: Those who are
accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that
an accident-prone person will have an accident at sometime within a fixed 1-year period with
probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It
is assumed that 30 percent of the human population is accident prone. Given this information,
answer the sub-questions.
The insurance company has to pay an insurance fee of Rs. 10 per accident if the accident happens
in the first year. If the company has sold 1000 insurances in total, then how much money (in Rs.)
will it expect to pay at the end of the first year for Class-2 people? (Note: Enter the answer **rounded**
**to two decimal places**. For example, if the answer is “Rs. 1.235”, **then enter it as “1.24”)**
Published solution
**1. Count expected Class-2 accidents:** Of 1000 policies, \(1000(0.70)=700\) belong to Class 2. Expected first-year accidents are \(700(0.20)=140\).
**2. Multiply by payout:** \(140(10)=1400.00\) rupees. This excludes Class-1 claims.
**Answer: 1400.00.**
**(The following is a purely imaginary scenario)**
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1.
Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two
decimal places. Eg: If your answer is 10.256, then round it to 10.26)
If a linear demand-response curve is fit for the data in Table-1, what is the satiating price for ice
creams? (Note: Enter the answer **rounded to two decimal places**. For example, if the answer is
“1.235”, **then enter it as “1.24”)**
Published solution
**1. Fit the exact linear relationship:** Each five-unit price increase lowers demand by 20, so the slope is −20/5=−4. Using (p,D)=(10,160), the intercept is 160+4(10)=200. Thus \(D(p)=200-4p\).
**2. Solve for zero demand:** \(0=200-4p\) gives satiating price \(p=50.00\).
**Answer: 50.00.**
**(The following is a purely imaginary scenario)**
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1.
Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two
decimal places. Eg: If your answer is 10.256, then round it to 10.26)
If a linear demand-response curve is fit for the data in Table-1, what is the market size for ice
creams? (Note: Enter the answer **rounded to two decimal places**. For example, if the answer is
“1.235”, **then enter it as “1.24”)**
Published solution
**1. Fit the exact linear relationship:** Each five-unit price increase lowers demand by 20, so the slope is −20/5=−4. Using (p,D)=(10,160), the intercept is 160+4(10)=200. Thus \(D(p)=200-4p\).
**2. Interpret the intercept:** Market size is the model’s demand at zero price, \(D(0)=200.00\).
**Answer: 200.00.**
**(The following is a purely imaginary scenario)**
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1.
Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two
decimal places. Eg: If your answer is 10.256, then round it to 10.26)
What is the elasticity of the linear demand-response curve, when the price is Rs. 35? (Note: Enter
the answer **rounded to two decimal places**. For example, if the answer is “1.235”, **then enter it as**
**“1.24”)**
Published solution
**1. Fit the exact linear relationship:** Each five-unit price increase lowers demand by 20, so the slope is −20/5=−4. Using (p,D)=(10,160), the intercept is 160+4(10)=200. Thus \(D(p)=200-4p\).
**2. Evaluate elasticity at p=35:** Demand is \(200-4(35)=60\). Elasticity magnitude is \(\varepsilon=4(35)/60=2.333333\), rounding to 2.33.
**Answer: 2.33.**
**Convention note:** The signed price elasticity is −2.33; the course reports its nonnegative magnitude.
**(The following is a partially imaginary scenario)**
The BA discourse is often cluttered with queries / requests related to solutions for Past Year
Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to
put in effort to find solutions by searching the discourse. However, the results seem to be
disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of
students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and
Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150
student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have
either “followed the instructions” or “not followed the instructions” or “have not accessed the
discourse at all” (these three are referred to as access categories). Specifically, for the sample data
in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was
observed that
1. For the **Male** sample: 30, 20, 35, 35, 45 and 35 had **not followed** the instructions respectively in
each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on)
2. For the **Male** sample: 20, 10, 15, 15, 15 and 10 had **not accessed discourse** at all respectively in
each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on)
3. For the **female** sample: 15, 22, 33, 25, 20 and 20 had **followed** the instructions respectively in
each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on)
4. For the **female** sample: 30, 20, 25, 25, 25 and 10 had **not accessed discourse** at all respectively
in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on)
Moreover, Dr. Milo assumes **that all learners in the “followed the instructions” category** are
Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing
the appropriate statistical test. Each term is a sample point.
Given this information, answer the
What is the probability that a specific term will fall in Bin-4 when performing the hypothesis test to
check if Dr. Milo’s assumption that all learners in the “followed the instructions” category are
Uniformly distributed? (Note: Enter the answer **rounded to two decimal places.** For example, if the
answer is “0.235”, **then enter it as “0.24”)**
Published solution
**1. Use equal probability areas:** Six equal-area bins partition total probability 1, so Bin-4 has probability \(1/6\approx0.166667\).
**2. Round the requested probability:** Enter 0.17.
**Answer: 0.17.**
**Convention note:** The exact 1/6 should be retained for expected-count calculations; using its rounded display value 0.17 would make six bin probabilities sum to 1.02.
**(The following is a partially imaginary scenario)**
The BA discourse is often cluttered with queries / requests related to solutions for Past Year
Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to
put in effort to find solutions by searching the discourse. However, the results seem to be
disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of
students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and
Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150
student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have
either “followed the instructions” or “not followed the instructions” or “have not accessed the
discourse at all” (these three are referred to as access categories). Specifically, for the sample data
in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was
observed that
1. For the **Male** sample: 30, 20, 35, 35, 45 and 35 had **not followed** the instructions respectively in
each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on)
2. For the **Male** sample: 20, 10, 15, 15, 15 and 10 had **not accessed discourse** at all respectively in
each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on)
3. For the **female** sample: 15, 22, 33, 25, 20 and 20 had **followed** the instructions respectively in
each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on)
4. For the **female** sample: 30, 20, 25, 25, 25 and 10 had **not accessed discourse** at all respectively
in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on)
Moreover, Dr. Milo assumes **that all learners in the “followed the instructions” category** are
Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing
the appropriate statistical test. Each term is a sample point.
Given this information, answer the
What will be the expected frequency in Bin-2 when performing the hypothesis test to check if Dr.
Milo’s assumption that all learners in the “followed the instructions” category are Uniformly
distributed? (Note: Enter the answer **rounded to two decimal places**. For example, if the answer is
“1.235”, **then enter it as “1.24”**)
Published solution
**1. Count sample points:** Each of the six terms contributes one observed followed-instruction total, so n=6.
**2. Calculate expected frequency:** Bin-2 has probability 1/6, hence \(E_2=6(1/6)=1.00\).
**Answer: 1.00.**
**Convention note:** Each expected frequency is only 1, so the usual large-sample chi-square calibration is unreliable. This does not change the arithmetic expected count.
**(The following is a partially imaginary scenario)**
The BA discourse is often cluttered with queries / requests related to solutions for Past Year
Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to
put in effort to find solutions by searching the discourse. However, the results seem to be
disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of
students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and
Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150
student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have
either “followed the instructions” or “not followed the instructions” or “have not accessed the
discourse at all” (these three are referred to as access categories). Specifically, for the sample data
in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was
observed that
1. For the **Male** sample: 30, 20, 35, 35, 45 and 35 had **not followed** the instructions respectively in
each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on)
2. For the **Male** sample: 20, 10, 15, 15, 15 and 10 had **not accessed discourse** at all respectively in
each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on)
3. For the **female** sample: 15, 22, 33, 25, 20 and 20 had **followed** the instructions respectively in
each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on)
4. For the **female** sample: 30, 20, 25, 25, 25 and 10 had **not accessed discourse** at all respectively
in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on)
Moreover, Dr. Milo assumes **that all learners in the “followed the instructions” category** are
Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing
the appropriate statistical test. Each term is a sample point.
Given this information, answer the
What is the value of the computed test statistic which will be used to check if Dr. Milo’s assumption
that all learners in the “followed the instructions” category are Uniformly distributed? (Note: Enter
the answer **rounded to two decimal places**. For example, if the answer is “1.235”, **then enter it as**
**“1.24”**)
A published solution is not available for this question yet.
**(The following is a partially imaginary scenario)**
The BA discourse is often cluttered with queries / requests related to solutions for Past Year
Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to
put in effort to find solutions by searching the discourse. However, the results seem to be
disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of
students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and
Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150
student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have
either “followed the instructions” or “not followed the instructions” or “have not accessed the
discourse at all” (these three are referred to as access categories). Specifically, for the sample data
in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was
observed that
1. For the **Male** sample: 30, 20, 35, 35, 45 and 35 had **not followed** the instructions respectively in
each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on)
2. For the **Male** sample: 20, 10, 15, 15, 15 and 10 had **not accessed discourse** at all respectively in
each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on)
3. For the **female** sample: 15, 22, 33, 25, 20 and 20 had **followed** the instructions respectively in
each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on)
4. For the **female** sample: 30, 20, 25, 25, 25 and 10 had **not accessed discourse** at all respectively
in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on)
Moreover, Dr. Milo assumes **that all learners in the “followed the instructions” category** are
Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing
the appropriate statistical test. Each term is a sample point.
Given this information, answer the
How many degrees of freedom is present for the hypothesis test used to check if Dr. Milo’s
assumption that all learners in the “followed the instructions” category are Uniformly distributed?
Published solution
**1. Count categories and fitted parameters:** There are six bins, and the uniform endpoints 4 and 75 are specified rather than estimated.
**2. Calculate nominal df:** \(df=6-1-0=5\).
**Answer: 5.**
**Convention note:** This is the nominal count. Expected frequencies of only one per bin do not support the usual chi-square approximation.
**(The following is a purely imaginary scenario)**
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the
sales are made at the Forenoon (FN). In the second marketplace, sales are made during the
Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth
marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the
four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer
the given subquestions.
The question of whether total sales in different marketplaces for product A and total sales in
different marketplaces for product B are independent across the different days is being checked.
Then what is the expected frequency for “Product-B” on “03-01-2025”? (Note: Enter the answer
**rounded to two decimal places**. For example, if the answer is “1.235”, **then enter it as “1.24”**)
Published solution
**1. Aggregate the four marketplaces within each date:** For the five dates, (A,B) totals are (78,155),(58,181),(74,185),(40,220),(40,202). Product totals are A=290 and B=943; overall N=1233.
**2. Apply independence:** On the third date, total sales are 74+185=259. Thus \[E_{\text{third date},B}=\frac{259(943)}{1233}\approx198.083536\to198.08.\]
**Answer: 198.08.**
**Convention note:** The question says 03-01-2025, while the source table lists 03-01-2023. The calculation uses the third date in the supplied table.
**(The following is a purely imaginary scenario)**
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the
sales are made at the Forenoon (FN). In the second marketplace, sales are made during the
Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth
marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the
four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer
the given subquestions.
The question of whether total sales in different marketplaces for product A and total sales in
different marketplaces for product B are independent across the different days is being checked.
Then what is the value of the computed test statistic? (Note: Enter the answer **rounded to two**
**decimal places**. For example, if the answer is “1.235”, **then enter it as “1.24”)**
Published solution
**1. Aggregate the four marketplaces within each date:** For the five dates, (A,B) totals are (78,155),(58,181),(74,185),(40,220),(40,202). Product totals are A=290 and B=943; overall N=1233.
**2. Calculate expected counts:** Expected (A,B) pairs are approximately (54.80,178.20),(56.21,182.79),(60.92,198.08),(61.15,198.85),(56.92,185.08).
**3. Sum cell deviations:** \[\chi^2=\sum_{i=1}^{5}\sum_{j=1}^{2}\frac{(O_{ij}-E_{ij})^2}{E_{ij}}\approx32.730391\to32.73.\]
**Answer: 32.73.**
**(The following is a purely imaginary scenario)**
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the
sales are made at the Forenoon (FN). In the second marketplace, sales are made during the
Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth
marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the
four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer
the given subquestions.
The question of whether total sales in different marketplaces for product A and total sales in
different marketplaces for product B are independent across the different days is being checked.
Then what is the number of degrees of freedom for the test? (Note: Enter the answer **rounded to**
**two decimal places**. For example, if the answer is “1.235”, **then enter it as “1.24”**)
A published solution is not available for this question yet.
