Imagine you are working alongside the marketing team of an e-commerce firm that is looking to increase its revenue

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Problem 1 (Convergence)

Prove the following.

(a) If 𝑋𝑋𝑛𝑛 = 𝑜𝑜𝑃𝑃(1), then 𝑋𝑋𝑛𝑛 = 𝑂𝑂𝑃𝑃(1).

 (b) If 𝑝𝑝

 𝑝,𝑝then 𝑋𝑋−1

 −1.

 𝑋𝑋𝑛𝑛 → 𝑐𝑐 > 0 𝑛𝑛    → 𝑐𝑐

(c) If 𝑋𝑋𝑛𝑛 ∼ 𝑁𝑁(cos(𝑛𝑛𝑛𝑛) , 1), then 𝑋𝑋𝑛𝑛 = 𝑂𝑂𝑃𝑃(1).

(d) If 𝑋𝑋𝑛𝑛 ∼ 𝑁𝑁(0, 𝑛𝑛), then 𝑋𝑋𝑛𝑛 ≠ 𝑂𝑂𝑃𝑃(1).

 Problem 2 (Insurance)

There is a 0.01% chance that a driver is involved in a car accident that results in a death per month. If that happens, the driver needs to pay $100,000. With the remaining probability 99.99%, nothing happens so the driver does not incur any cost. An insurance company provides a liability insurance that fully covers the payment at the insurance premium $40 per month. In order to reduce the chance of being insolvent to be less than 0.15%, how many customers does the insurance company have to have? Use the central limit theorem.

 

Problem 3 (Customer Service Management)

As a CCO (Chief Customer Officer), you are renewing the operation of a call center for a telecom company. One of the main complaints for the past year has been that the wait time is too long. While increasing the staff is one solution to this, the CEO rejects this option for cost consideration. To mitigate the pain during the wait time, you instead seek to introduce the callback option. With this new system, an incoming caller is given an option to wait for a callback in a certain time range of your choice. This way, customers can do other things while waiting, and you hope that this leads to reduction of the complaints about the wait time. On the other hand, if you fail to give callback in the specified time range, you are afraid that this creates a new set of complaints about callbacks being late. To avoid this, you want to make sure that 84% of all the callbacks are made within the promised time window. The internal data suggest that 90% of the incoming calls take 5 min of service time while 10% take 15 min. If there are 9 callers in queue, how long should the system tell the caller that the callback takes? Use the central limit theorem.

 

Problem 4 (Marketing)

Choose the best option to answer each question.

(a) Imagine you are working alongside the marketing team of an e-commerce firm that is looking to increase its revenue. One of the analysts tells you that she has statistically tested the revenue lift associated with a recent marketing campaign. She mentions that she has found that the campaign had a statistically significant impact on revenue. What does significance mean here when size = 5%?

i. The campaign was effective for 95% of customers.

ii. There is a very low variance on the estimated size of the campaign effect.

iii. The 95% confidence interval does not contain 0.

iv. The estimated campaign effect is far from zero.

(b) Suppose the marketing analyst is used to presenting 95% confidence intervals, but you want complete certainty over the effectiveness of the campaign, because it is very costly. What does a 100% confidence interval look like?

i. It is not possible to form a 100% confidence interval.

ii. It will basically be the same interval as the 95% confidence interval.

iii. The confidence interval would cover every possible value from negative infinity to positive infinity.

iv. Start with the 95% confidence interval and make the endpoints 5% more extreme on each end.

(c) It turns out that the p-value for the analyst’s test is 0.049. What does this mean?

i. If the campaign is ineffective, there was only 4.9% chance that she would have obtained as low a p-value as this one.

ii. If the campaign is ineffective, the probability of her finding it effective is 4.9%.

iii. We can only be 4.9% confident that the campaign was effective.

iv. The test was ineffective for 4.9% of the customers.

 

 

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme