Question

Due to uncertain economic conditions the owners of an independent bookstore estimate the following probabilities for moderate growth, the status quo and recession for next year and their associated profits for each scenario. What is their expected profit for next year?

(Imagine this as a table)

Growth, Probability, Estimated Profit
Moderate Growth, 0.35, $250,000
Status Quo, .45, $200,000
Recession, .20, $100,000


Answer 1

I'm imagining

Answer 2

;)

Answer 3

Expected profit is the goal, and luckily the owners of the bookstore have you given you probabilities for the profits to earn in each economic condition scenario

Answer 4

Because the next year could enter either of the 3 economic condition scenarios, you will multiply each expected profit by its respective probability, then sum those 3 values to obtain the expected profit for the next year.

Answer 5

oh. how did you know that?

Answer 6

Because you dealing with expectations. This idea of expected value is prominent in finance and economics.

Because there are 3 ways the economy could go: moderate growth, recession, status quo, you also don't know which of the 3 ways will be the true way. So, there is probability assigned to each way.

If things go to moderate growth, then you will definitely make $250,000
If things go to status quo, then you will definitely make $200,000
If things go to recession, then you will definitely make $100,000

But these are all conditionals.

Answer 7

:D thanks flan! this was so so helpful.

Answer 8

Right, so to imagine the profit you will make while considering the 3 directions of the economy, you sum up the profits multiplied by their respective probabilities of economic direction.

No problem, glad to help

Answer 9

@sleestak By the way, I recommend changing your avatar/profile picture ;)

Answer 10

oh. OK. I'll do that now.

Answer 11

consider your table as a probability mass function,the question is asking for the expected profit or in other words the expected mean given by the formula below