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Statistics and Probability Mean and Variance of Random Variable / Normal Random Variable 600SHS 2. VARIANCE AND STANDARD DEVIATION OF DISCRETE RANDOM VARIABLE Find the Variance and Standard Deviation of the following. a. Rafael plays a gambling game where it is possible to lose $2.00, break even, win $4.00, or win $15.00 each time he plays. The probability distribution for each outcome is provided by the following table: Outcome -$2.00 $0.00 $4.00 $15.00 Probability 0.30 0.40 0.20 0.10 b. Suppose that the casino decides that the game does not have an impressive enough top prize with the lower payouts, and decides to double all of the prizes, as follows: Outcome -$5.00 -$1.00 $6.00 $10.00 Probability 0.25 0.35 0.25 0.15 c. As in the case of the mean, consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. The resulting distribution is the following Outcome -$6.00 -$3.00 $6.00 $12.00 Probability 0.30 0.40 0.20 0.10