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You are an analyst with an investment firm. A California developer is offering an investment that may return the following amounts at the end of the next eight years: Year$1$: $$100,000$ Year$2$: $$120,000$ Year$3$: $$100,000$ Year$4$: $$110,000$ Year$5$: $$100,000$ Year$6$: $$130,000$ Year$7$: $$100,000$ Year$8$: $$90,000.$ The investment may also return in lower returns or losses as follows: Year$1$: $$10,000$ Year$2$: $$80,000$ Year$3$: $$-10,000$ Year$4$: $$100,000$ Year$5$: $$80,000$ Year$6$: $$0$ Year$7$: $$90,000$ Year$8$: $$70,000$ Each payment has a BERNOULLI distribution with the higher payment occuring with probability $1-$A; the lower payment $($or loss$)$ occurs with probability A$.$ The payments are probabilistically independent.

Alternatively, a Florida developer is offering an investment that may return the following amounts at the end of each of the next $10$ years: Year$1$: $$180,000$ Year$2$: $$160,000$ Year$3$: $$90,000$ Year$4$: $$210,000$ Year$5$: $$100,000$ Year$6$: $$130,000$ Year$7$: $$100,000$ Year$8$: $$90,000$ Year$9$: $$100,000$ Year$10$: $$90,000.$ The investment may also result in lower returns or losses as follows: Year$1$: $$70,000$ Year$2$: $80,000$ Year$3$: $$-70,000$ Year$4$: $$100,000$ Year$5$: $$80,000$ Year$6$: $$1,000$ Year$7$: $$90,000$ Year$8$: $$70,000$ Year$9$: $$60,000$ Year$10$: $$85,000.$ Each payment has a Bernoulli distribution with the higher payment occuring wiht probability B$,$ the lower payment occurs with probability $1-$B$.$ The payments are probabilistically independent. Using $8\%$ rate of return, which investment do you advise your firm to make. Fully explain your answer and show all work. There is no one correct answer here but your adivce should include the expected present value for each possible investment and its variance.

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