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Science Forum

  1. 13 Feb '15 10:29 / 2 edits
    I was trying to study probability density function by reading:

    http://en.wikipedia.org/wiki/Probability_density_function

    after reading:

    "...(2 hour−1)×(1 nanosecond) = 6×10−13...."

    (the "10−13" above was written as 10 to the power of -13 and the "hour−1" was written as hour to the power of -1 so to mean "per hour", but this post doesn't seem to allow me to copy and post that here like it should be )

    and spending some time confused trying to understand where on earth does the "6" and the "-13" come from, I have concluded that this is almost certainly an error and that should have been:

    "...(2 hour−1)×(1 nanosecond) = 2×10−9...."

    Can I have confirmation that I am right about that?

    But, what I really want to know is, how do I contact wikipedia to make them correct such an error?
    -I wouldn't like other readers to be confused by such error like I was as this is frustrating.
  2. 13 Feb '15 10:42
    Originally posted by humy
    But, what I really want to know is, how do I contact wikipedia to make them correct such an error?
    It is Wikipedia. You do not contact them. You make sure you are correct, then you look up near the top of the page for 'edit' and you make the correction yourself.
  3. 13 Feb '15 10:52 / 1 edit
    Originally posted by humy
    "...(2 hour−1)×(1 nanosecond) = 2×10−9...." .
    I am not sure where the 6 came from, but:
    5+ 0.01 hours corresponds to 2% (which is 0.02)
    therefore:
    5+ 10e-9 hrs corresponds to 2 * 10e-13
  4. 13 Feb '15 16:10
    You can freely edit Wikipedia. If your edit is wrong then someone is likely to revert the change. However, if you frequently make incorrect edits it is likely your editing privileges will be revoked (Wikipedia has revoked these privileges for many high schools, for instance).
  5. 13 Feb '15 18:33 / 3 edits
    Originally posted by twhitehead
    I am not sure where the 6 came from, but:
    5+ 0.01 hours corresponds to 2% (which is 0.02)
    therefore:
    5+ 10e-9 hrs corresponds to 2 * 10e-13
    5+ 0.01 hours corresponds to 2% (which is 0.02)

    yes, and you got that from:

    “What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is "2%" “

    That implies a probability density of 0.02 per 0.01 hours at 5 hours. A probability density of 0.02 per 0.01 hours is the same as a probability density of 2 per hour Because 0.02/0.01 = 2. So the probability density at 5 hours is 2 per hour in this case which is where the “(2 hour−1)” came from in that link.

    (Obviously, then, the: “2” in the “(2 hour−1)” in “(2 hour−1)×(1 nanosecond) = 6×10−13. “ in that link is not directly referring to a percentage and that 2% but rather it is referring to a probability density of 2 per hour -just in case anyone here got slightly confused by that )

    therefore:
    5+ 10e-9 hrs corresponds to 2 * 10e-13

    You mean the probability of the event happening ( the bacterium dies in this case ) in the interval of time of
    [ 5 hrs, 5 + 10e-9 hrs ] is 2 * 10e-13.


    I have just realized I have made an error! In my calculations, I simply completely forgot to take into account that there are 3600 seconds in an hour!

    One nanosecond is 10e-9 of a second which, because there are 3600 seconds in an hour, is approximately (to 5 decimal places) 2.77778 * 10e-13 of an hour. Well that explains where the link got that that “-13” exponent! So I was wrong about that!

    BUT, now we have the “(2 hour−1)×(1 nanosecond) = “ in the link equalling the probability density of 2 multiplied by 2.77778 * 10e-13 which approximately equals 5.55556 * 10e-13 which the author of the link must have rounded off to 6 * 10e-13 so the link was about right! But one could still criticized the link for not indicating that this is an approximation and for not showing the workings to make it clear where that “6 * 10e-13” came from.

    So, although the link was correct, I think I could edit it to make it a lot clearer and less confusing on these points.
  6. 13 Feb '15 18:42
    Actually, I think you are correct and it should be e-9.
  7. 13 Feb '15 18:57 / 3 edits
    Originally posted by twhitehead
    Actually, I think you are correct and it should be e-9.
    Actually, I just realized I was completely wrong! read my correction on my last post.

    So the link was technically correct after all! But the fact that we were BOTH confused by it shows that the link is not very clear and could do with just a bit of re-editing to make it clearer. I may do that in due course ( extremely carefully )
  8. 13 Feb '15 19:03
    Originally posted by KazetNagorra
    You can freely edit Wikipedia. If your edit is wrong then someone is likely to revert the change. However, if you frequently make incorrect edits it is likely your editing privileges will be revoked (Wikipedia has revoked these privileges for many high schools, for instance).
    Don't worry; I will always check and double check.
  9. 13 Feb '15 19:03
    Originally posted by twhitehead
    It is Wikipedia. You do not contact them. You make sure you are correct, then you look up near the top of the page for 'edit' and you make the correction yourself.
    Arr, I didn't notice that tiny edit tab up there!
  10. 13 Feb '15 19:07 / 7 edits
    On an unrelated maths problem (although still to do with probability ) :

    Is there a way of simplifying the RHS expression in the equation:

    y = ( x ^ n ) * ( ( 1 – x ) ^ ( e – n ) )

    ?

    ( don't know if this has any relevance but, for the application I have in mind, both n and e are natural numbers while x is a continuous random variable in the [0, 1] interval and y is necessarily always a positive real number and, perhaps slightly confusingly, represents a probability density of other possible probabilities! )

    I am trying to make it a bit easier for myself to finds its integral.
  11. 13 Feb '15 19:43
    Originally posted by humy
    I have just realized I have made an error! In my calculations, I simply completely forgot to take into account that there are 3600 seconds in an hour!
    Wow. I totally missed that too.
  12. 13 Feb '15 19:44
    Originally posted by humy
    Don't worry; I will always check and double check.
    Do consider adding some clarifying calculation to the page.
  13. 13 Feb '15 20:10
    I just spotted an edit error on that link!
    it says:

    "...Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is "2%". Next: What is the probability that the bacterium lives between 5 hours and 5.001 hours? The answer is probably around 0.2%, since this is 1/10th of the previous interval. The probability that the bacterium lives between 5 hours and 5.0001 hours is about 0.02%, and so on...."

    The two times it says "lives" above should be "dies" to correspond to the first time it said "dies". This is one of the corrections I will be making.
  14. 13 Feb '15 22:04 / 2 edits
    I have now carefully edited all the changes in:

    http://en.wikipedia.org/wiki/Probability_density_function

    All the changes I made are in the "Example" section only.
    Does everyone approve?
    The main change there I made is replace where it previously said:

    "Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is "2%". Next: What is the probability that the bacterium lives between 5 hours and 5.001 hours? The answer is probably around 0.2%, since this is 1/10th of the previous interval. The probability that the bacterium lives between 5 hours and 5.0001 hours is about 0.02%, and so on.

    Therefore, in response to the question "What is the probability that the bacterium lives 5 hours?", a literally correct but unhelpful answer is "0", but a better answer is (2 hour−1) dt. This is the probability that the bacterium dies within a small (infinitesimal) window of time around 5 hours, where dt is the duration of this window. For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour−1)×(1 nanosecond) = 6×10−13.
    The quantity 2 hour−1 is called the probability density for the bacterium to live 5 hours. ..."

    with:

    "..Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is "2%". Next: What is the probability that the bacterium dies between 5 hours and 5.001 hours? The answer is probably around 0.2%, since this is 1/10th of the previous interval. The probability that the bacterium dies between 5 hours and 5.0001 hours is about 0.02%, and so on.

    Because, for example, a probability of 2% is the same as a probability of 0.02, and because, for example, the interval of time between 5 hours and 5.01 hours is 0.01 hours (i.e. 1% of an hour), the probability that the bacterium dies between, for example, 5 hours and 5.01 hours being 2% can be said to have what it called a probability density of 2 per hour because (0.02 probability)/(0.01 hours) is 2 per hour. The probability density at 5 hours can be written as (2 hour−1) dt where the quantity 2 hour−1 is the probability density for the bacterium to live 5 hours and where dt is the duration of an arbitrarily very small window of time around 5 hours.

    Therefore, in response to the question "What is the probability that the bacterium lives 5 hours?", a literally correct but unhelpful answer is "0", but a better answer can be written as (2 hour−1) dt. This is the probability that the bacterium dies within a small (infinitesimal) window of time around 5 hours, where dt is the duration of this window. For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour−1)×(1 nanosecond) which, because there are 3600 seconds in an hour and there are a billion nanosecond in a second, is (2 hour−1)×(1 nanosecond) = 2 × 10−9 / 3600 ≃ 5.556×10−13...."
  15. 14 Feb '15 17:24
    Originally posted by twhitehead
    It is Wikipedia. You do not contact them. You make sure you are correct, then you look up near the top of the page for 'edit' and you make the correction yourself.
    ...and get it turned back by someone with more ignorance but also more Jimmy-Points than you have.

    Yeah, good luck with that.