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# Entropy and Probabilities watch

1. 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.

2. How many possible outcomes are there when two dice are thrown? How many of these add to 7?
3. 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)

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?
5. ic, so is this correct?

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

And you already worked out that the probability of the total being 7 is 6/36=1/6. So you're done.
7. (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) ?
8. (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
9. 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 with probabilities respectively is:

Your question seems to be about information but your answer seems to be about entropy. Which is it?
10. (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 with probabilities respectively is:

Your question seems to be about information but your answer seems to be about entropy. Which is it?
hmm.. Isn't Entropy == Information?
11. 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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