Calculate the variance and standard deviation in the given case.

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 .10, .50 and .40. Payoff is $500, 100 and 0. net Profit is $400, 0 and -100. What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return.

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