Statistics
posted by Emilia .
A scratchcard 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?

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) = _______