Question

In: Statistics and Probability

your aunt comes to you with an investment opportunity. She needs you to invest $500,000. If...

your aunt comes to you with an investment opportunity. She needs you to invest $500,000. If the investment succeed, it will pay you back your investment plus an additional $2 million. If it fails you get nothing back. She thinks there is a 30% chance of success.

a. what is the expected value of the investment?

b. what is the most likely outcome?

Solutions

Expert Solution

a.

Returns(X) Probability(P) XP
Success           7,000,000 0.30    2,100,000
Failure 0 0.70 0
Expected value ==>    2,100,000

b. Most likely outcome: Expected value = $ 1,867,600 ( As per following calculation)

Returns(X) Probability(P) XP
Success           7,000,000 0.2668    1,867,600
Failure 0 0.7332 0
Expected value ==>    1,867,600

To find most likely outcome:

The following simulation of 9 trials using Binomial distribution was conducted and we find most likely

probability of success = 0.2668.

Trials Probability of success
1                                0.1211
2                                0.2335
3                    0.2668
4                                0.2001
5                                0.1029
6                                0.0368
7                                0.0090
8                                0.0014
9                                0.0001

orchestra answered 2 years ago
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