Respuesta :
Using a discrete probability distribution to model the situation, we have that:
i. The expected value of the amount you win is of -$0.06676.
ii. The variance of the amount you win is of 0.1211$².
What is the distribution that models the situation?
Considering you can win with black and yellow balls, the probability of getting two balls off the same color is given by:
p = 2 x 5/10 x 4/9 = 0.4444.
Hence the distribution of the earnings is given by:
- P(X = 1.1) = 0.4444.
- P(X = -1) = 0.5556.
What is the mean of a discrete distribution?
The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Hence:
E(X) = 1.1 x 0.4444 - 1 x 0.5556 = -$0.06676.
The expected value of the amount you win is of -$0.06676.
What is the variance of a discrete distribution?
The expected value of a discrete distribution is given by the sum of the differences squared between each outcome and the mean, multiplied by it's respective probability.
Hence:
V(X) = (1.1 - (-0.06676))² x 0.4444 - (1 - 0.06676)² x 0.5556 = 0.1211$².
The variance of the amount you win is of 0.1211$².
More can be learned about discrete probability distributions at https://brainly.com/question/24802582
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