Question

A scratch-card costs 5¤ and has two possible prizes. There is a 10% chance you get 5¤ back and a 1% chance you get 100¤. In all other cases, you get nothing. Let X denote your net winnings, i.e, (X = prize - cost). What are the expectation and standard deviation of X?

Answer 1

E(X) = (5¤ - 5¤) * 10% + (100¤ - 5¤) * 1% + (0¤ - 5¤) * 89%
E(X) = 0 * 10% + (95) * 1% + (-5) * 89%
= -3.5¤

SD(X) = √ [ (0 - (-3.5)) ² * 10% + (95 - (-3.5)) ² * 1% + (-5 - (-3.5)) ² * 89%]
SD(X) = _______