An investor is considering a $30,000 investment in a start-up company. She estimates that she has a probability of 0.30 of a $20,000 loss, probability of 0.20 of a $35,000 profit, probability of 0.35 of a $45,000 profit, and probability 0.15 of breaking even (a profit of $0). What is the expected value of the profit? Would you advise the investor to make the investment? Explain why?

X      -20000   35000   45000    0

P(X)      0.3         0.2       0.35     0.15

And we can find the expected value with the following formula:

And after apply this formula we got:

And for this case since the expected value for the profit >0 then we can conclude that the investor could do the investment

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.  

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).  

Solution to the problem

For this case we define the random variable X as = the amount of money that we expect to win or loss and we have the following distribution given:

X      -20000   35000   45000    0

P(X)      0.3         0.2       0.35     0.15

And we can find the expected value with the following formula:

And after apply this formula we got:

And for this case since the expected value for the profit >0 then we can conclude that the investor could do the investment

she will travel a distance in the range of 3 - 11 miles