Consider a game in which the player loses $5 with probability 1/2, breaks even with probability...
Consider a game in which the player loses $5 with probability 1/2, breaks even with probability 1/3, and wins $10 with probability 1/6. Construct a probability distribution to represent this game. Also find the mean, variance and standard deviation.
Homework Answers
The probability distribution is summarized in the following table:
| Winning (x) | P[X=x] |
| -5 | 1/2 |
| 0 | 1/3 |
| 10 | 1/6 |
Now,
Mean = E[X] = x.p(x)
= -5*1/2 + 0*1/3 + 10*1/6
= -5/2 + 5/3
= -5/6
Variance= E[X2] - (E[X])2
E[X2] = x2.p(x)
= (-5)2*1/2 + 0*1/3 +102 *1/6
= 25/2 + 50/3
= 175/6
So, Variance = 175/6 -(-5/6)2
= 175/6 -25/36
= 1025/6
Standard deviation =
=
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