What does E(X) mean and how do I calculate E(X)?

• E(X)?means the?expected value?or the?mean?of a?random variable X
  • The expected value does not need to be an obtainable value of?X
  • For example: the expected value number of times a coin will land on tails when flipped 5 times is 2.5
• For a?discrete?random variable, it is calculated by:

• • • This is given in the?formula booklet
• Look out for?symmetrical?distributions (where the values of X are symmetrical and their probabilities are symmetrical) as the mean of these is the same as the median
  • For example: if X can take the values 1, 5, 9 with probabilities 0.3, 0.4, 0.3 respectively then by symmetry the mean would be 5

How can I decide if a game is fair?

• Let?X?be the random variable that represents the?gain/loss?of a player in a game
  • X?will be?negative?if there is a?loss
• Normally the expected gain or loss is calculated by?subtracting?the?cost to play?the game from the?expected value?of the?prize
• If E(X) is?positive?then it means the player can?expect to make a gain
• If E(X) is?negative?then it means the player can?expect to make a loss
• The game is called?fair?if the?expected gain is 0
  • E(X) = 0