Expected Value - rFronteddu/general_wiki GitHub Wiki

When talking about expected value, we have to consider that the experimental probability we get from experiments approximates the often unknown theoretical true probability.

• $P(A)=\frac{successful trials}{all trials}$
• For categorical values, the expected value of an experiment is then E(A) = P(A) * n
  • example: P(aces of spades) = 0.25, E(A) = 0.25 * 20 = 5. We expect to see the AoS 20 times if we draw 20 times from a full deck of cards.
• For numerical values in a sample a, b, c ⇒ E(A) = a * P(a) + b * P(b) + c * P(c)
  • ex. Throwing darts:
    • center = 100 points with prob 0.1
    • first ring 20 with prob 0.4
    • third ring 10 with prob 0.1.
    • ⇒ E(score) = 0.5 * 10 + 0.4 * 20 + 0.1 * 100 = 23.
    • Note that even if 23 is not a number we can get, we can use it to obtain a range of predictability.