Question

A venture capitalist, willing to invest $1,000,000, is considering an investment in a biotech firm. They have a 10% chance of returning $6,000,000 profit, a 70% of no profit orloss, and a 20% chance of losing the million dollars. Let x represent profit (in dollars) from the investment. Construct a discrete probability distribution and compute the exactexpected profit. (Consider a loss of one million dollars as a negative amount.)The expected profit E(x) is:

Answer 1

We have to calculate the expected profit of the investment.

The variable x represents the random discrete variable.

The outcomes and their probability are:

$\begin{gathered} x_1=6\to P(x_1)=0.1 \\ x_2=0\to P(x_2)=0.7 \\ x_3=-1\to P(x_3)=0.2 \end{gathered}$

NOTE: we expressed the profit in millions of dollars to simplify.

We then can calculate the expected profit as:

$\begin{gathered} E(x)=\sum_{n\mathop{=}1}^3x_iP(x_i) \\ E(x)=0.1\cdot6+0.7\cdot0+0.2\cdot(-1) \\ E(x)=0.6+0-0.2 \\ E(x)=0.4 \end{gathered}$

As E(x) = 0.4 and this corresponds to $400,000.

Answer: The expected profit is E(x) = 400,000.