Consider a game in which a participant pays $2 to roll a die. The participant receives $3 if they roll a 1 (i. e. they go up by a
$1) and they receive $4 if they roll a 6 (i. e. they go up by $2).
If they roll any other number they lose their $2 (i. e. they lost
$2).
What is the average expected monetary value of a single roll?