Assignment - Statistics questions and would require layman explanation for the questions.
(a) Describe each component in the probability space. Why is there a need to include the sigma-field in the probability space?
(b) Let X be a uniform random variable on the interval [-1, 1]. Determine the p.d.f of X and E(X). Also, consider Y = 2X + 4. Evaluate E(Y).
(c) Appraise the statement: "When measuring the centrality of the random variable, it is best to consider the expectation of the random variable".
(d) Explain and discuss the intuition behind the approach that you would implement to evaluate if X and Y are independent.
(e) Carefully describe one statistical approach you would implement to determine the association between house prices in Singapore and Hong Kong. What do you think their association looks like and what are its possible drivers?