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lgbasallote

  • 2 years ago

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?

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  1. hartnn
    • 2 years ago
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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)

  2. lgbasallote
    • 2 years ago
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    hmmm....

  3. UnkleRhaukus
    • 2 years ago
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    uniform probability distribution eh,

  4. lgbasallote
    • 2 years ago
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    ^?

  5. UnkleRhaukus
    • 2 years ago
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    and i suppose that , measurements are in 0.l L, or are they in 0.5 L units?

  6. lgbasallote
    • 2 years ago
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    what do you mean?

  7. UnkleRhaukus
    • 2 years ago
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    well if the millage was 7.45 does that get counted as 7.5 ?

  8. tkhunny
    • 2 years ago
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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).

  9. lgbasallote
    • 2 years ago
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    i don't think so

  10. lgbasallote
    • 2 years ago
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    @tkhunny i don't believe in bad questions....

  11. UnkleRhaukus
    • 2 years ago
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    but you post so many bad questions lgba

  12. tkhunny
    • 2 years ago
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    If it's a legitimate question p(7.5) = 0 for any CONTINUOUS distribution.

  13. lgbasallote
    • 2 years ago
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    why so?

  14. lgbasallote
    • 2 years ago
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    @UnkleRhaukus no question is bad to those who see clearly

  15. UnkleRhaukus
    • 2 years ago
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    but you havent provided enough information to answer this question, once again

  16. lgbasallote
    • 2 years ago
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    that's what you think

  17. lgbasallote
    • 2 years ago
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    there are actually enough information

  18. lgbasallote
    • 2 years ago
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    so much so that tkhunny is right

  19. UnkleRhaukus
    • 2 years ago
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    what are the increments in milage ?

  20. lgbasallote
    • 2 years ago
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    you look for too much information

  21. tkhunny
    • 2 years ago
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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?

  22. lgbasallote
    • 2 years ago
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    hmm i don't see how that turns out to be 0 though

  23. UnkleRhaukus
    • 2 years ago
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    in real situation milage is a measured quantity, and it will come in incremental values

  24. tkhunny
    • 2 years ago
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    You didn't answer my question. Do you see how those two probabilities are calculated?

  25. lgbasallote
    • 2 years ago
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    would it be because of the integral?

  26. lgbasallote
    • 2 years ago
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    i did answer your question

  27. tkhunny
    • 2 years ago
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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).

  28. lgbasallote
    • 2 years ago
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    geometry is boring though...

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

  30. lgbasallote
    • 2 years ago
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    or was it for odd...

  31. tkhunny
    • 2 years ago
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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.

  32. lgbasallote
    • 2 years ago
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    oh...yeah....

  33. lgbasallote
    • 2 years ago
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    i suck in calculus

  34. UnkleRhaukus
    • 2 years ago
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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 \(\text dx\)

  35. tkhunny
    • 2 years ago
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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.

  36. lgbasallote
    • 2 years ago
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    @UnkleRhaukus there are no increments

  37. tkhunny
    • 2 years ago
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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.

  38. lgbasallote
    • 2 years ago
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    class? there's no class...

  39. tkhunny
    • 2 years ago
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    That does make it harder to discuss things in class, then, doesn't it?!

  40. lgbasallote
    • 2 years ago
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    not class as in etiquette...

  41. UnkleRhaukus
    • 2 years ago
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    \[\frac1n\sum{\Delta x} \longrightarrow\frac 1n\int\text dx\]

  42. lgbasallote
    • 2 years ago
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    ...no increments.....

  43. UnkleRhaukus
    • 2 years ago
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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

  44. lgbasallote
    • 2 years ago
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    yes...

  45. lgbasallote
    • 2 years ago
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    0...

  46. UnkleRhaukus
    • 2 years ago
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    yes . bad question

  47. lgbasallote
    • 2 years ago
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    you just overcomplicate things

  48. lgbasallote
    • 2 years ago
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    you assume data...bad answer

  49. UnkleRhaukus
    • 2 years ago
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    math maps reality , reality is complicated,

  50. lgbasallote
    • 2 years ago
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    that's your opinion

  51. UnkleRhaukus
    • 2 years ago
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    then answer to your Hypothetical question is Useless , they answer to my variation on your question is not useless

  52. tkhunny
    • 2 years ago
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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!

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