The probabilities are 022 036 028 and 014 that an investor w

The probabilities are 0.22, 0.36, 0.28, and 0.14 that an investor will be able to sell a piece of property at a profit of $2,500, at a profit of $1,500, at a profit of $500, or at a loss of $500, respectively.

A) Let X the profit for each sell. Construct a table that has the level of X and the corresponding probability, i.e., the probability distribution.

B) Construct a table for F(X).

C) What is the investor\'s expected profit?

D) What is the probability that the investor\'s profit is greater than $500?

Solution

A)

X ......2500.......1500........500.........-500

P(x)....0.22........0.36........0.28........0.14

B)

F(x),,,,,,0.22.......0.58........0.86........1

where F(x) is the cumulative probability

C)

expected profit = sum[ X * P(X)]

= 0.22 * 2500 + 0.36 * 1500 + 0.28 * 500 + 0.14 * -500

= 1160

D)

P(X>500) = P(X=1500) + P(X=2500)

= 0.22 + 0.36

= 0.58