Question

1. Suppose that you are thinking about whether to invest in a new
business venture. You believe that there are three possible outcomes if you decide to invest:
• Make a profit of $100,000
• Make a profit of $20,000
• Lose $50,000
Suppose that you consider the probability of making a profit of $100,000 to be .15, and you
consider it three times more likely that you make a profit of $20,000.
a) Determine the expected value of your net profit from thisinvestment.
b) Write a sentence interpreting what this expected value means in this context.
c) Report the probability that your net profit would exceed its expected value if you were
to make this investment once.

Answer 1

Answer:

a)

The PMF of net profit is,

P(X = 100,000) = 0.15

P(X = 20,000) = 0.15 * 3 = 0.45

P(X = -50,000) = 1 - (0.15 + 0.45) = 0.4

Expected value =

= 100,000 * 0.15 + 20,000 * 0.45 - 50,000 * 0.4

= $4000

b)

If you invest in the new business venture, the net profit is $4000 in the long run.

c)

Probability that the net profit would exceed the expected value = P(X > 4000)

= P(X = 100,000) + P(X = 20,000)

= 0.15 + 0.45

= 0.60

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