HTML Developer

Project Description

Problem 1: Stock Market and Dice Rolls (15 points)
Analyze expected values and variances for different investment strategies and dice games:(a) Investing in one stock.
(b) Diversifying across multiple stocks.
(c) Choosing a strategy aligned with risk preferences.
(d) Expected value and variance of a dice roll.
(e) Expected value and variance when payoffs are cube values of dice rolls.

Problem 2: Propositions with Logical Variables (10 points)
Evaluate probabilities in logical propositions:(a) Expected number of true propositions.
(b) Proof of existence of variable assignments making all propositions true.

Problem 3: Laundry Delay Scenarios (20 points)
Calculate expected delays for students based on different conditions:(a) Busy students completing problem sets.
(b) Relaxed students rolling dice daily.
(c) Unlucky students recovering based on dice rolls.
(d) Overall expected delay considering all student types.

Problem 4: Identifying Coins (10 points)
Determine the number of coin tosses needed to identify whether a coin is fair or biased (95% confidence).

Problem 5: Exam Scoring Process (13 points)
Analyze the expected scores for exams graded by:(a) TAs (based on structured scoring).
(b) Lecturers (based on dice rolls and impressions).
(c) Overall exam scores.

Problem 6: Random Ball Allocation in Boxes (32 points)
Study probabilities and expected outcomes in random processes:(a) Probability distribution for empty boxes.
(b) Expected number of empty boxes.
(c) Probability of multiple balls in a single box.
(d) Maximum number of balls in a box.
(e) Asymptotic conclusions about ball distribution.
This assignment requires applying probability theory, statistical analysis, and logical reasoning.