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lgbasallote Group Title

Fuel mileage is uniformly distributed between 5 km/L to 12 km/L. What is the probability that on the next trip, fuel mileage is 7.5 km/L?

  • one year ago
  • one year ago

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  1. hartnn Group Title
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    the probability distribution function is 1/(12-5) as seen from earlier question so for any mileage between 5 and 12, the probability will be 1/(12-5)

    • one year ago
  2. lgbasallote Group Title
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    hmmm....

    • one year ago
  3. UnkleRhaukus Group Title
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    uniform probability distribution eh,

    • one year ago
  4. lgbasallote Group Title
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    ^?

    • one year ago
  5. UnkleRhaukus Group Title
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    and i suppose that , measurements are in 0.l L, or are they in 0.5 L units?

    • one year ago
  6. lgbasallote Group Title
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    what do you mean?

    • one year ago
  7. UnkleRhaukus Group Title
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    well if the millage was 7.45 does that get counted as 7.5 ?

    • one year ago
  8. tkhunny Group Title
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    Very bad question. Two things wrong with it. 1) The probability of anything on the "next" trip is quite dependent on the nature of the next trip. Will you be going east or west in Eastern Wyoming? It makes a very big difference! The expected value of gas mileage on a randomly selected trip would be a better question. 2) More importantly, it's a continuous distribution. The probability of a single value is ZERO (0).

    • one year ago
  9. lgbasallote Group Title
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    i don't think so

    • one year ago
  10. lgbasallote Group Title
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    @tkhunny i don't believe in bad questions....

    • one year ago
  11. UnkleRhaukus Group Title
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    but you post so many bad questions lgba

    • one year ago
  12. tkhunny Group Title
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    If it's a legitimate question p(7.5) = 0 for any CONTINUOUS distribution.

    • one year ago
  13. lgbasallote Group Title
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    why so?

    • one year ago
  14. lgbasallote Group Title
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    @UnkleRhaukus no question is bad to those who see clearly

    • one year ago
  15. UnkleRhaukus Group Title
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    but you havent provided enough information to answer this question, once again

    • one year ago
  16. lgbasallote Group Title
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    that's what you think

    • one year ago
  17. lgbasallote Group Title
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    there are actually enough information

    • one year ago
  18. lgbasallote Group Title
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    so much so that tkhunny is right

    • one year ago
  19. UnkleRhaukus Group Title
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    what are the increments in milage ?

    • one year ago
  20. lgbasallote Group Title
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    you look for too much information

    • one year ago
  21. tkhunny Group Title
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    hartnn was close. This distribution can be modelled as a rectangle. It's width is 7, the distance from 5 to 12. Thus, it's height must be 1/7. The probability that mileage will be between 5 and 6 can be read from the rectangle. It's a smaller rectangle of length 1 (6-5) and height 1/7. The probability that mileage will be greater than 8 can be read from the rectangle. It's a smaller rectangle of length 4 (12-8) and height 1/7. Do you see how this works?

    • one year ago
  22. lgbasallote Group Title
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    hmm i don't see how that turns out to be 0 though

    • one year ago
  23. UnkleRhaukus Group Title
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    in real situation milage is a measured quantity, and it will come in incremental values

    • one year ago
  24. tkhunny Group Title
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    You didn't answer my question. Do you see how those two probabilities are calculated?

    • one year ago
  25. lgbasallote Group Title
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    would it be because of the integral?

    • one year ago
  26. lgbasallote Group Title
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    i did answer your question

    • one year ago
  27. tkhunny Group Title
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    You can talk integrals if you want, but a Uniform Distribution is easier. Geometry is sufficient. Given a single value, the width of the rectangle is zero (0). The height is still 1/7. The integral shoudl make it clear, though: \[\int\limits_{7.5}^{7.5} \frac{1}{7} dx = ?? \] Don't evaluate this integral. It is an eyeball problem. With the limits identical, it is zero (0).

    • one year ago
  28. lgbasallote Group Title
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    geometry is boring though...

    • one year ago
  29. lgbasallote Group Title
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    by the way...i thought \[\int \limits_a^a f(x)dx\] is 0 only when f(x) is even?

    • one year ago
  30. lgbasallote Group Title
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    or was it for odd...

    • one year ago
  31. tkhunny Group Title
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    No. That makes no sense. Get that our of your head. It is zero. You are thinking of [-a,a] for odd functions. This is [a,a]. It's zero if it exsits at all.

    • one year ago
  32. lgbasallote Group Title
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    oh...yeah....

    • one year ago
  33. lgbasallote Group Title
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    i suck in calculus

    • one year ago
  34. UnkleRhaukus Group Title
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    if milage is measured in 0.5 Km/L increments then there are 14 possible out comes, and the probability of milage being 7.5 Km/L will be 1/14, if milage is measured in 0.1 Km/L then there are 70 possible out comes, and the probability of milage being 7.5 Km/L will be 1/70, as the increments \(\Delta x\) , get smaller and smaller , they approach \(\text dx\)

    • one year ago
  35. tkhunny Group Title
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    Time to stop sucking! More focus. Seems to me, after this brief exposure, that you are a little random about it. Just organize your thinking a little better.

    • one year ago
  36. lgbasallote Group Title
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    @UnkleRhaukus there are no increments

    • one year ago
  37. tkhunny Group Title
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    If mileage is measured in 0.5 Km/L increments, you have written your own problem statement and not answered the question that is asked. I will grant, however, that this may have been additional information shared in class.

    • one year ago
  38. lgbasallote Group Title
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    class? there's no class...

    • one year ago
  39. tkhunny Group Title
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    That does make it harder to discuss things in class, then, doesn't it?!

    • one year ago
  40. lgbasallote Group Title
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    not class as in etiquette...

    • one year ago
  41. UnkleRhaukus Group Title
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    \[\frac1n\sum{\Delta x} \longrightarrow\frac 1n\int\text dx\]

    • one year ago
  42. lgbasallote Group Title
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    ...no increments.....

    • one year ago
  43. UnkleRhaukus Group Title
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    then you get zero, BUT you really should has specified that the increments are infinitesimals in the question if you wanted people to know what you ment

    • one year ago
  44. lgbasallote Group Title
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    yes...

    • one year ago
  45. lgbasallote Group Title
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    0...

    • one year ago
  46. UnkleRhaukus Group Title
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    yes . bad question

    • one year ago
  47. lgbasallote Group Title
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    you just overcomplicate things

    • one year ago
  48. lgbasallote Group Title
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    you assume data...bad answer

    • one year ago
  49. UnkleRhaukus Group Title
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    math maps reality , reality is complicated,

    • one year ago
  50. lgbasallote Group Title
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    that's your opinion

    • one year ago
  51. UnkleRhaukus Group Title
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    then answer to your Hypothetical question is Useless , they answer to my variation on your question is not useless

    • one year ago
  52. tkhunny Group Title
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    You converted me, @UncleRhaukus. On an exam, I would answer this qeustion two ways. 1) Point out the obvious "definition" question that results int eh value zero (0), and 2) Quantize the distribution in some way, as you have done, clearly document me assumptions, and provide some sort of non-zero response. Of course, not everyone can do that on every question. If it was multip-choice and zero (0) wasn't on there, I would cry foul!

    • one year ago
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