Question

Creating a discrete probability distribution: A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a social media company, has a 20% chance of returning $7,000,000 profit, a 30% chance of returning no profit, and a 50% chance of losing the million dollars. The second company, an advertising firm has a 10% chance of returning $3,000,000 profit, a 60% chance of returning a $2,000,000 profit, and a 30% chance of losing the million dollars. The third company, a chemical company has a 40% chance of returning $3,000,000 profit, a 50% chance of no profit, and a 10% chance of losing the million dollars. a. Construct a Probability Distribution for each investment. This should be 3 separate tables (See the instructors video for how this is done) In your table the X column is the net amount of profit/loss for the venture capitalist and the P(X) column uses the decimal form of the likelihoods given above. b. Find the expected value for each investment. c. Which investment has the highest expected return? d. Which is the safest investment and why? e. Which is the riskiest investment and why?

Answer 1

a) Let X be the  net amount of profit/loss for the venture capitalist.

The first investment, a social media company, has a 20% chance of returning X$7,000,000 profit,

X=$7,000,000 with a probability of 0.20, that is  P(X=7000000)=0.20

a 30% chance of returning no profit,

X=$0 with a probability of 0.30, that is  P(X=0)=0.30

and a 50% chance of losing the million dollars.

X=-$1,000,000 with a probability of 0.50, that is  P(X=-1000000)=0.50

ans: Probability Distribution for the first investment is

X	P(X)
7,000,000	0.2
0	0.3
-1,000,000	0.5

The second company, an advertising firm has a 10% chance of returning $3,000,000 profit,

X=$3,000,000 with a probability of 0.10, that is  P(X=3000000)=0.10

a 60% chance of returning a $2,000,000 profit,

X=$2,000,000 with a probability of 0.60, that is  P(X=2000000)=0.60

and a 30% chance of losing the million dollars

X=-$1,000,000 with a probability of 0.30, that is  P(X=-1000000)=0.30

Ans: The probability distribution for the second investment is

Advertising Firm
X	P(X)
3,000,000	0.1
2,000,000	0.6
-1,000,000	0.3

The third company, a chemical company has a 40% chance of returning $3,000,000 profit,

X=$3,000,000 with a probability of 0.40, that is  P(X=3000000)=0.40

a 50% chance of no profit,

X=$0 with a probability of 0.50, that is  P(X=0)=0.50

and a 10% chance of losing the million dollars

X=-$1,000,000 with a probability of 0.10, that is  P(X=-1000000)=0.10

ans: The probability distribution for the third investment is

Chemical company
X	P(X)
3,000,000	0.4
0	0.5
-1,000,000	0.1

b) The expected value of profit for the first investment is

ans: The expected value of profit for the first investment is $900,000

The expected value of profit for the second investment is

ans: The expected value of profit for the second investment is $1,200,000

The expected value of profit for the third investment is

ans: The expected value of profit for the third investment is $1,100,000

c) ans: We can see that the second investment has the highest expected return

d) The risk is indicated by the standard deviation (or variance) of profit. We will find the standard deviation of profit for each of the investments

The expected value of for the first investment is

The standard deviation of profit for the first investment is

The expected value of for the second investment is

The standard deviation of profit for the second investment is

The expected value of for the third investment is

The standard deviation of profit for the third investment is

d) We can see from the above that the second investment has the lowest standard deviation of profit.

ans:  the second investment is the safest investment as it has the lowest standard deviation (or the variance) of profit.

e) We can see from the above that the first investment has the highest standard deviation of profit.

ans:  the first investment is the riskiest investment as it has the highest standard deviation (or the variance) of profit.