The random variable X is a payout table of a casino slot machine. The probability mass...

Question

Question

The random variable X is a payout table of a casino slot machine. The probability mass function is given:

X	-5	0	2	10	20	40	60	1000
Probability	0.65	0.159	0.10	0.05	0.02	0.01	0.01	0.001

Find the variance for the payout .

Answer 1

Answer #1

Mean = X * P(X)

= -5 * 0.65 + 0 * 0.159 + 2 * 0.10 + 10 * 0.05 + 20 * 0.02 + 40 * 0.01 + 60 * 0.01 + 1000 * 0.001

= -0.15

Variance = X² * P(X) - Mean²

= [ -5² * 0.65 + 0² * 0.159 + 2² * 0.10 + 10² * 0.05 + 20² * 0.02 + 40² * 0.01 + 60² * 0.01 + 1000² * 0.001 - (-0.15)²

= 1081.6275

Answer 2

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