Casino payout X in rupees has distribution: −100 with probability 0.25; 0 with 0.50; 100 with 0.20; 500 with 0.05. Find standard deviation in rupees, nearest integer.
Mean is $E[X]=-100(0.25)+100(0.20)+500(0.05)=20$. Second moment is $E[X^2]=10000(0.25)+10000(0.20)+250000(0.05)=17000$. Variance is 17000−20² = 16600 and standard deviation is √16600 = 128.84, rounding to Rs. 129.
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