3. Consider a property market where the price of your apartment is mod- elled by a binomial random variable. Under current market conditions, the probability that the value of your apartment increases in value by 5% (of its original value) in one month is 0.45. The probability that it decreases in value by 5% (of its original value) in one month is 0.55. Given your past experience with lockdowns and apartment living, you decide to relocate to a regional area in 6 months time. Let X denote the number of increases in the price of your apartment over these 6 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the percentage change in the price of your apartment. Then Y = 0.05.X-0.05(6 - X) because 0.05.X is the total percentage increase in price and 0.05(6- X) is the total percentage decrease in price. Simplify the expres- sion for Y in terms of X. Then using (a), find E(Y) and (Y).

3. Consider a property market where the price of your apartment is mod- elled by a binomial random variable. Under current market conditions, the probability that the value of your apartment increases in value by 5% (of its original value) in one month is 0.45. The probability that it decreases in value by 5% (of its original value) in one month is 0.55. Given your past experience with lockdowns and apartment living, you decide to relocate to a regional area in 6 months time. Let X denote the number of increases in the price of your apartment over these 6 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the percentage change in the price of your apartment. Then Y = 0.05.X-0.05(6 - X) because 0.05.X is the total percentage increase in price and 0.05(6- X) is the total percentage decrease in price. Simplify the expres- sion for Y in terms of X. Then using (a), find E(Y) and (Y).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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