Erd diagram

MSc in Foundations of Data Science University of Hertfordshire

Maths Competition

Description:

In this competition, each group needs to finish the following two tasks:

Task 1.

Consider the function 𝑓𝑋(𝑥) = { 4 + 𝑥 − 5𝑥2 if 0 ≤ 𝑥 ≤ 1

0 otherwise

Is there a random variable 𝑋 which has this as its density? • You must show your justification.

• If your answer is Yes, then you need to compute the expected value of 𝑋, that is 𝐸(𝑋). • If your answer is No, then you need to give a solution to remedy the function 𝑓𝑋(𝑥) so

that there is a random variable 𝑋 which has it (the remedied function) as its density.

Task 2.

Your task is to generate a question to test if a student understands one of the two concepts in

the following bullet points and provide your solution to the question. You are free to choose

which one you want to work on. You must show how the question is generated via the Group

Discussions page. The question should inspire others to think about it and should help other

students to understand the concept.

Through this task, you will develop your ability to ask mathematical questions. “Without

questions, there would be no mathematics, and unless students learn to ask questions, they

cannot operate as mathematicians.” [1].

• Given the definition of derivative as follows [2],

what mathematical question can you ask?

• Given the definition of definite integral as follows [3],

what mathematical question can you ask?

Timeline

Noon 18/12/2020 final submission deadline.

Submission Instruction

1. Each group prepares one and only one submission.

2. The submission including solutions to those two tasks should be a PDF file.

3. The submission should be done via Canvas.

Evaluation

Submissions will be judged by a panel consisting of 3 tutors: Emil Dmitruk, Felix Riegler and

Agnes Bonivart, with Emil Dmitruk being the chair, based on the following criteria:

1. Group collaboration: Do group members participate actively? Are discussions within the

group supportive and efficient?

2. Correctness of your solution to Task 1.

3. Quality of Task 2: whether the proposed question is valid and inspiring to others, and

whether the provided answer is correct.

4. Clarity of the writing.

The panel will announce the result on 08/01/2021.

References

1. C. Foster: Student-Generated Questions in Mathematics Teaching, Mathematics Teacher, 105 (1):

26-31, 2011.

2. Credit: https://tutorial.math.lamar.edu/classes/calci/defnofderivative.aspx

3. Credit:

https://tutorial.math.lamar.edu/classes/calci/defnofdefiniteintegral.aspx#:~:text=The%20definite%

20integral%20is%20defined,notation%20for%20an%20indefinite%20integral.