Find the Expected value or Mean of the following. Show your complete solution. Rafael plays a gambling game where it is possible to lose $2.00, break-even, win $4.00, or win $15.00 each time he plays. The probability distribution for each outcome is provided by the following table: Outcome -$2.00 $0.00 $4.00 $15.00 Probability 0.30 0.40 0.20 0.10 Suppose that the casino decides that the game does not have an impressive enough top prize with the lower payouts, and decides to double all of the prizes, as follows: Outcome -$5.00 -$1.00 $6.00 $10.00 Probability 0.25 0.35 0.25 0.15 As in the case of the mean, consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. The resulting distribution is the following: Outcome -$6.00 -$3.00 $6.00 $12.00 Probability 0.30 0.40 0.20 0.10

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

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Find the Expected value or Mean of the following. Show your complete solution.

Rafael plays a gambling game where it is possible to lose $2.00, break-even, win $4.00, or win $15.00 each time he plays. The probability distribution for each outcome is provided by the following table:

Outcome -$2.00 $0.00 $4.00 $15.00

Probability 0.30 0.40 0.20 0.10

Suppose that the casino decides that the game does not have an impressive enough top prize with the lower payouts, and decides to double all of the prizes, as follows:

Outcome -$5.00 -$1.00 $6.00 $10.00

Probability 0.25 0.35 0.25 0.15

As in the case of the mean, consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. The resulting distribution is the following:

Outcome -$6.00 -$3.00 $6.00 $12.00

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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