Recognitions:
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## Probability of 0 bit in ASCII text files

 Quote by Cylab C: combinations Pr[0] = 9/16. X: number of ASCII bits , from which N is taken. case: N1=7 & N2=4 . Assume N is taken from X bits, which is ASCII. Other definitions should be clear
You wrote (9X/16)C2, and you have still offered no reasonable explanation for that notation. Did you mean (9/16)XC2?

 Quote by haruspex You wrote (9X/16)C2, and you have still offered no reasonable explanation for that notation. Did you mean (9/16)XC2?
X: The number of bits in ASCII.
9X/16: The number of 0 bits in the X that are classified as successes.
7 or 4: The number(s) of bits taken consecutively from X.
2: The number of 2 zeros in the 7 or 4 that are classified as successes.
(9X/16)C2 : The number of combinations of 9X/16, taken two 0 bits at a time.

Recognitions:
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 Quote by Cylab X: The number of bits in ASCII. 9X/16: The number of 0 bits in the X that are classified as successes. 7 or 4: The number(s) of bits taken consecutively from X. 2: The number of 2 zeros in the 7 or 4 that are classified as successes. (9X/16)C2 : The number of combinations of 9X/16, taken two 0 bits at a time.
Now that you have explained that, thankyou, I can see where it is wrong.
For one thing, that analysis treats all bits as independently 0 or 1, regardless of their proximity to each other. Bits multiples of 8 positions apart will be positively correlated, and at other distances negatively correlated.
More significantly, let's look at what these represent:
1st. (N1 case) : {(9X/16)C2 * (7X/16)C5 } / xC7.
1st. (N2 case) : {(9X/16)C2 * (7X/16)C2 } / xC4.
The first is the probability of picking 7 bits that are exactly two 0 bits and 5 1 bits; the second is the prob of picking 4 bits that are exactly 2 and 2. No wonder they're different! In the problem I thought we were discussing, P[00] doesn't care what the remaining 2 or 5 bits are.

 Quote by haruspex Now that you have explained that, thankyou, I can see where it is wrong. For one thing, that analysis treats all bits as independently 0 or 1, regardless of their proximity to each other. Bits multiples of 8 positions apart will be positively correlated, and at other distances negatively correlated. More significantly, let's look at what these represent: 1st. (N1 case) : {(9X/16)C2 * (7X/16)C5 } / xC7. 1st. (N2 case) : {(9X/16)C2 * (7X/16)C2 } / xC4. The first is the probability of picking 7 bits that are exactly two 0 bits and 5 1 bits; the second is the prob of picking 4 bits that are exactly 2 and 2. No wonder they're different! In the problem I thought we were discussing, P[00] doesn't care what the remaining 2 or 5 bits are.
You are right!
P[00] doesn't care what the remaining 2 or 5 bits are.
So does the calculation in the following two cases, which are the prob of P[00] taken from N1 and N2 respectively regardless of the contents of the N1 & N2.
1st. (N1 case) : {(9X/16)C2 * (7X/16)C5 } / xC7.
1st. (N2 case) : {(9X/16)C2 * (7X/16)C2 } / xC4.

Recognitions:
Homework Help
 Quote by Cylab So does the calculation in the following two cases, which are the prob of P[00] taken from N1 and N2 respectively regardless of the contents of the N1 & N2. 1st. (N1 case) : {(9X/16)C2 * (7X/16)C5 } / xC7. 1st. (N2 case) : {(9X/16)C2 * (7X/16)C2 } / xC4.
Once again, I'm not at all sure what you are saying. Are you insisting that the above formulae are correct for P[00]? I have just explained to you why they are not.

 Quote by haruspex Once again, I'm not at all sure what you are saying. Are you insisting that the above formulae are correct for P[00]? I have just explained to you why they are not.