A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. a. Construct a PDF for each investment.

b. Find the expected value for each investment.

c. Which is the safest investment? Why do you think so?

d. Which is the riskiest investment? Why do you think so?

e. Which investment has the highest expected return, on average?

a. Construction of PDF (Probability Distribution Function) for each investment:

Software Company:

x                        P(x)

$5,000,000    0.10

$1,000,000     0.30

-$1,000,000    0.60

Hardware Company:

x                        P(x)

$3,000,000    0.20

$1,000,000     0.40

-$1,000,000    0.40

Biotech Firm:

x                        P(x)

$6,000,000     0.10

$0                     0.70

-$1,000,000    0.20

b. Expected value for each investment:

Software Company:

x                        P(x)   Expected value (xP(x)

$5,000,000    0.10       $500,000

$1,000,000     0.30        300,000

-$1,000,000    0.60      -600,000

Total expected value  $300,000

Hardware Company:

x                        P(x)   Expected value (xP(x)

$3,000,000    0.20         $600,000

$1,000,000     0.40           400,000

-$1,000,000    0.40         -400,000

Total expected value     $600,000

Biotech Firm:

x                        P(x)   Expected value (xP(x)

$6,000,000     0.10      $600,000

$0                     0.70     $0

-$1,000,000    0.20      -200,000

Total expected value  $400,000

c. The safest investment is the investment in the Hardware Company.  Here, the probability of success is highest, with 60%.

d. The riskiest investment is the investment in the Software Company where the probability of failure is highest, with 60%.

e. The investment with the highest expected return on average is the investment in the Hardware Company.  It has a total expected return of $600,000.

Step-by-step explanation:

a) Data and Calculations:

Investment amount = $1,000,000

Investment Options:

Software Company:

10% chance of returning $5,000,000

30% chance of returning $1,000,000

60% chance of losing $1,000,000

Hardware Company:

20% chance of returning $3,000,000

40% chance of returning $1,000,000

40% chance of losing $1,000,000

Biotech Firm:

10% chance of returning $6,000,000

70% chance of no profit or loss

20% chance of losing $1,000,000

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2