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    Any forumers know how to solve this?

    The sum of the faces of 2 normal dices when thrown is 7. How much information does this fact supply us with (The outcome such as (1,6) and (6,1) are different )? Explain.

    Thanks in advance
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    How many possible outcomes are there when two dice are thrown? How many of these add to 7?
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    possible outcomes = (1,6) (6,1) (2,5) (5,2) (3,4) (4,3)
    is 6.

    Total outcomes = 6 x 6 = 36

    I don't really understand what this line means (How much information does this fact supply us with)
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    It's asking

    How much information does the statement "the sum of the faces of 2 normal dices when thrown is 7" provide us with in determining that the combinations such as "1,6" and "6,1" are different?
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    ic, so is this correct?

    Entropy = 6 * -(1/36)log(1/36) ?
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    The information of an event E with probability of occurrence p is:

    I(E)= - \log_2 (p)

    And you already worked out that the probability of the total being 7 is 6/36=1/6. So you're done.
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    (Original post by yagmai)
    ic, so is this correct?

    Entropy = 6 * -(1/36)log(1/36) ?
    Dear guys, is my working correct?

    Each outcome probability is 1/36. Entropy of 1 outcome is -(1/36)log(1/36). Since there are 6 outcomes, Entropy = 6 * -(1/36)log(1/36) ?
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    (Original post by yagmai)
    Dear guys, is my working correct?

    Each outcome probability is 1/36. Entropy of 1 outcome is -(1/36)log(1/36). Since there are 6 outcomes, Entropy = 6 * -(1/36)log(1/36) ?

    Any experts can verify if my working is correct? Thanks
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    Hang on. I'm getting confused as what you're asking and what you're writing as your answer are not connected.

    My understanding is as follows:

    The information of an event (in this case I think the event is "rolling two dice and the sum being 7") is as I described 3 posts ago.

    The entropy of a random variable (so not just a single event) taking values x_1, x_2, \ldots, x_n with probabilities p_1, p_2, \ldots, p_n respectively is:
    \displaystyle H(X) = - \sum_{i=1}^n p_i \log_2 (p_i)

    Your question seems to be about information but your answer seems to be about entropy. Which is it?
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    (Original post by SsEe)
    Hang on. I'm getting confused as what you're asking and what you're writing as your answer are not connected.

    My understanding is as follows:

    The information of an event (in this case I think the event is "rolling two dice and the sum being 7") is as I described 3 posts ago.

    The entropy of a random variable (so not just a single event) taking values x_1, x_2, \ldots, x_n with probabilities p_1, p_2, \ldots, p_n respectively is:
    \displaystyle H(X) = - \sum_{i=1}^n p_i \log_2 (p_i)

    Your question seems to be about information but your answer seems to be about entropy. Which is it?
    hmm.. Isn't Entropy == Information? :confused:
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    Entropy is the expected information gained on knowing the outcome of a random variable.

    http://en.wikipedia.org/wiki/Information_entropy
    "In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable."

    http://en.wikipedia.org/wiki/Information_content
    "self-information is a measure of the information content associated with the outcome of a random variable."

    In this case we have the outcome of a random variable.
 
 
 
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