Suppose an individual plays a gambling game where it is possible to lose $1.00, break even, win $3.00, or win $10.00 each time she plays. The following table provides the probability distribution for each outcome: Outcome -$1.00 $0.00 $3.00 $10.00 Probability 0.30 0.40 0.20 0.10
Suppose an individual plays a gambling game where it is possible to lose $1.00, break even, win $3.00, or win $10.00 each time she plays. The following table provides the probability distribution for each outcome: Outcome -$1.00 $0.00 $3.00 $10.00 Probability 0.30 0.40 0.20 0.10
Suppose an individual plays a gambling game where it is possible to lose $1.00, break even, win $3.00, or win $10.00 each time she plays. The following table provides the probability distribution for each outcome: Outcome -$1.00 $0.00 $3.00 $10.00 Probability 0.30 0.40 0.20 0.10
Suppose the casino decides to adjust the payout levels by subtracting $1.00 from each prize. Find the mean and the variance of the outcome
Transcribed Image Text:Suppose an individual plays a gambling game where it is possible to lose $1.00, break even,
win $3.00, or win $10.00 each time she plays. The following table provides the probability
distribution for each outcome:
Outcome
-$1.00 $0.00
$3.00
$10.00
Probability
0.30
0.40
0.20
0.10
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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