Consider the experiment of rolling five (5) dice, each with 19 sides numbered 1 through 19, where each die is fair, i.e. the sample space consists of equally likely outcomes. Compute the expected sum of the four dice with the highest values. For example, after rolling, the dice show 2, 10, 4, 2, and 13. Since 2 is the lowest value showing on these dice, the sum in this case is 2 + 10 + 4 + 13 29. We gave two approaches to a similar problem in class: • An inefficient algorithm for computing the expected value. • An efficient computation using linearity of expected value. Either method is fine, but consider the larger potential for rounding error using the algorithm. Such error is completely avoidable using either method, however, so your answer is expected to be accurate to four decimal places.
Consider the experiment of rolling five (5) dice, each with 19 sides numbered 1 through 19, where each die is fair, i.e. the sample space consists of equally likely outcomes. Compute the expected sum of the four dice with the highest values. For example, after rolling, the dice show 2, 10, 4, 2, and 13. Since 2 is the lowest value showing on these dice, the sum in this case is 2 + 10 + 4 + 13 29. We gave two approaches to a similar problem in class: • An inefficient algorithm for computing the expected value. • An efficient computation using linearity of expected value. Either method is fine, but consider the larger potential for rounding error using the algorithm. Such error is completely avoidable using either method, however, so your answer is expected to be accurate to four decimal places.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Consider the experiment of rolling five (5) dice, each with 19 sides numbered 1 through 19,
where each die is fair, i.e. the sample space consists of equally likely outcomes.
Compute the expected sum of the four dice with the highest values. For example, after
rolling, the dice show 2, 10, 4, 2, and 13. Since 2 is the lowest value showing on these
dice, the sum in this case is 2 + 10 + 4 + 13 = 29.
We gave two approaches to a similar problem in class:
• An inefficient algorithm for computing the expected value.
• An efficient computation using linearity of expected value.
Either method is fine, but consider the larger potential for rounding error using the
algorithm. Such error is completely avoidable using either method, however, so your
answer is expected to be accurate to four decimal places.
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