6.2 Expected Value Flashcard

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Multiply each possible outcome by its probability, and add each product together.

A discrete random variable is one that can take on a countable number of distinct values.

A continuous random variable can take on an infinite number of values within a given range.

The probability of landing on 4 is $$\frac{2}{5}$$ since there are 2 sections with 4 out of 5 total sections.

You would expect it to land on 4 approximately 30 times, calculated as $$75 \times \frac{2}{5} = 30$$ .

Expected profit = (Selling Price - Cost Price) x Number of Units Sold.

The expected profit per car is $3,500, calculated as $24,500 - $21,000.

The expected value is calculated as $$(-5 \cdot 0.4) + (1 \cdot 0.35) + (8 \cdot 0.25) = -2 + 0.35 + 2 = -1.65$$ .

It means the outcomes can be counted and are distinct, such as the number of heads when tossing coins.