Estimating Expected Value of a Random Variable X from 129 Rolls of a Dice

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Homework Help Overview

The discussion revolves around estimating the expected value and variance of a random variable X, defined as the sum of outcomes from rolling a single die 129 times. Participants are exploring the implications of Chebyshev's inequality in this context and questioning the clarity of the problem setup.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to clarify whether the problem involves rolling one die or multiple dice and are questioning how to calculate the expected value E(X) and variance Var(X) for the sum of the outcomes. There is also a focus on understanding the probability density function fX(x) for the sum.

Discussion Status

The discussion is ongoing, with some participants providing clarifications about the terminology used (die vs. dice) and expressing confusion about the calculations needed for expected value and variance. There is no explicit consensus yet, but participants are engaging with the problem and seeking to clarify assumptions.

Contextual Notes

Participants have noted the ambiguity in the problem statement regarding the terminology of "die" and "dice," which may affect the interpretation of the expected value and variance calculations. There is an emphasis on showing work before receiving further assistance.

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Pour an ordinary dice 129 times and let X the sum of all indications that it brings.

Let p=P(X<=12)

What is the minimum upper bound for the probability p resulting from inequality of Chebyshev;

Note: The probability density of X is symmetric about the mean value of X


how i can find the fX(x) of the sum of all indications that brings the dice if we roll it 129?
 
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ParisSpart said:
Pour an ordinary dice 129 times and let X the sum of all indications that it brings.

Let p=P(X<=12)

What is the minimum upper bound for the probability p resulting from inequality of Chebyshev;

Note: The probability density of X is symmetric about the mean value of X


how i can find the fX(x) of the sum of all indications that brings the dice if we roll it 129?

The question is unclear. Do you toss a single die 129 times (each time getting a number from 1 to 6), or do you toss a pair of dice 129 times (each time getting a number from 2 to 12)?

Anyway, you need to show your work first before we can help.
 
we toss a dice 129 times, but i can't think how to find the E(X) and Var(X) of this that's why i aksed for help...
i will estimate any sum? from 1 to 129?
 
ParisSpart said:
we toss a dice 129 times, but i can't think how to find the E(X) and Var(X) of this that's why i aksed for help...
i will estimate any sum? from 1 to 129?

You still have not described your problem in meaningful terms: the words "a dice" are contradictory. The "a" means one but the word "dice" means 2 or more. If you toss just one cube with faces numbered 1--6 you are tossing one die (NOT dice); if you toss two such cubes (giving a total from 2--12 in each toss) you are throwing dice = more than one die. So, which do you mean?
 
we toss one dice 129 times not two...
 
ParisSpart said:
we toss one dice 129 times not two...

No, you don't. You toss one die 129 times. You are tossing a DIE, not DICE.
 
yea anyway , how i am going to estimate the expected value of the random variable X which is the sum of all outcomes i am confused
 

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