A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100.
Probability Payoff Net Profit
.1 0 $500 $400
.50 1 00 0
.40 0 -1 00
What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return.