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?
Expectation E(x) is the sum of the products of the revenue/gain multiplied by the probability of the outcome.
Here we have three possible outcomes.
1.
5¤ at 10%, product=0.1*5¤=0.5¤
2.
100¤ at 1%, product=0.01*100¤ =1¤
3.
nothing at 89%, product=0¤ *0.89=0¤
E(x)=Sum=(0.5+1+0)¤ =1.5¤