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This is based on Week 1 and Week 2 information and is due January 20, 2024.

(6 marks) An experiment explores the correlation between study habits and success (a pass) in academic subjects.

(a) (2) What is the probability of someone succeeding in Math? Econ? Marketing?

(b) (2) What is the probability of passing Economics conditional on consistent study? inconsistent study?

(c) (2)Are study habits and academic success independent of each other? Provide a rationale for your answer.

(8) Given the following probability density function of X:

Also, Xi ∼ (µX, σX 2 ) and X is the sample mean. (2;10;4)

(a) Find an expression in terms of n, µX and σX for E(X 2 ). Show working.

(b) Using the given probability distribution, if n = 40, find a numerical solution.

(c) Assume there are 40 students tasked with the completion of a puzzle, each with a finishing time in minutes. Let’s say Xi represents the time it takes for student i to finish the puzzle. Assume each student’s finishing time is independent and has the probability distribution f(x) given above. If X is how long it takes, on average, for the students to finish the puzzle, what is the probability that, on average, a student’s finishing time is less than 20 minutes, using the central limit theorem and the results from part (b)?

From the text (5th edition): (8;6;12;18)

2.4 (b), (d; first sentence), (You can do it by hand, or in R/Python, but either way, working or code must be shown)

2.6 (a) - (c)

2.7

2.28 (a)-(d) (You are required to do this question in R or Python and submit the knitted PDF which you can merge with the previous section.)