Expected Value of a Random Variable | Why a Die Averages 3.5

What is the expected value of a random variable? Roll a die many times and the average of the results settles near 3.5. Why exactly 3.5: in N rolls each face comes up about N/6 times, N cancels, and what is left is each value times its probability, added up. That is the expected value, the balance point of the distribution. Then a dice game (is it worth playing, and what prize would make it fair), the properties E(X + c), E(kX), E(X + Y), and the sum of two dice. Animated on the board: no voice, just the mathematics. 0:00 Rolling a die: what is the average roll? 0:13 Random variable 0:46 The average of many rolls 1:13 Why 3.5 1:31 Expected value 2:11 The balance point 2:40 Is the game worth playing? 3:20 A fair game 3:39 Properties 3:57 Two dice 4:35 Summary #probability #expectedvalue #math #statistics #tutor