The return (dividend) of a share of stock is randomly distributed with 5 differe

Question

The return (dividend) of a share of stock is randomly distributed with 5 different outcomes possible as listed in the table below: Calculate the following: a. E(x) = mu (the population mean) b. sigma^2_x (the population variance) c. sigma_x (the population standard deviation d. An investor buys the stock and over the next 25 years (N = 25) the investor earns an annual average return of x bar = 7.5. The investor decides to sell the stock if the probability of earning an average return less than or equal to 7.5 is less than 10%. i. What is the probability of x bar lessthanorequalto 7.5 given N = 25 and the mu and sigma_x as calculated above? Should the investor sell? ii. What is the probability of the stock earning an average return greater than 11 given N = 25 and the mu and sigma_x as calculated above? iii. What is the probability of earning an average return between 7.5 and 11 given N = 25 and the mu and sigma_x as calculated above?

Explanation / Answer

mean = 1.4

variance = 3.3 - 1.4^2

= 1.34

standard deviation = sqrt(variance)

= 1.1576

x p(x) x*p(x) x^2*p(x) 0 0.25 0 0 1 0.35 0.35 0.35 2 0.2 0.4 0.8 3 0.15 0.45 1.35 4 0.05 0.2 0.8 1 1.4 3.3

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