Dice throw, avg.,standard deviation

Thread starter Pushoam
Start date Sep 11, 2017
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deviation Dice

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SUMMARY

The discussion centers on calculating the average and standard deviation of a dice throw using the formulas for expected value and variance. The expected value, denoted as , is calculated as the sum of the outcomes divided by the number of outcomes, yielding = 3.5 for a fair six-sided die. The variance is derived from the formula - ^2, leading to a standard deviation of approximately σ_x ≈ 1.291. The calculations and formulas provided are confirmed to be correct.

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Understanding of probability theory
Familiarity with expected value calculations
Knowledge of variance and standard deviation concepts
Basic algebra skills for manipulating equations

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Study the concept of expected value in probability distributions
Learn about variance and its significance in statistics
Explore the Central Limit Theorem and its applications
Practice calculating standard deviation with different probability distributions

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Students in statistics or probability courses, educators teaching statistical concepts, and anyone interested in understanding the mathematical principles behind dice games and random events.

Sep 11, 2017

Pushoam

Homework Statement

Homework Equations

The Attempt at a Solution

Let's denote the result of the throw by the variable x.
## <x> = Σ_i P_i x_i , i = 1,2,3,...,6.
\\= \frac{1+2+3+4+5+6}{6}
\\<x^2> = \frac{1^2+2^2+3^2+4^2+5^2+6^2}{6}
\\σ_x = \sqrt{<x^2> - <x>^2} ##
Is this correct?

Last edited: Sep 11, 2017

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Sep 11, 2017

jambaugh

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Your formulas appear to be correct.
you should get a standard deviation of the form: ##\sigma_x \approx ## *.**7825.

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