Let’s try calculating the expected values for a different activity. Suppose you are throwing a die. You’ve defined X as the number obtained upon throwing it once. By calculations, you find that the expected value for this is 3.5. Let’s see what our simulations show:

Recall that the expected value of a player’s winnings after playing our game once was ₹11.28. We said that reducing the prize money and/or increasing the penalty for our game might make the expected value negative. Let’s see how much we need to reduce or increase the prize money by.

Recall the problem you saw earlier, where we were asked by a company to suggest whether it should invest in a given project or not. We had made this probability distribution for X, the net revenue of the project:

X (Net Revenue of Project, in ₹ Crore) | P(x) |

-305 | 0.1 |

+15 | 0.7 |

+95 | 0.2 |

Now we are in a position to find the expected value for X, the return of the project. This is called the **expected return.** If it comes out to be negative, we can say that the project is not worth investing in.

The expected value of X, which is also called the expected return, is equal to:

(-305) * P(X = -305) + (+15) * P(X = +15) + (+95) * P(X = +95) = (-305) * 0.1 + (+15) * 0.7 + (+95) * 0.2 = -₹1 crore.

So, the expected return of the project is -₹1 crore. Hence, we can conclude that the project is not worth investing in.

You can find more examples of expected returns here.