lgbasallote
  • lgbasallote
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?
Mathematics
jamiebookeater
  • jamiebookeater
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hartnn
  • hartnn
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)
lgbasallote
  • lgbasallote
hmmm....
UnkleRhaukus
  • UnkleRhaukus
uniform probability distribution eh,

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lgbasallote
  • lgbasallote
^?
UnkleRhaukus
  • UnkleRhaukus
and i suppose that , measurements are in 0.l L, or are they in 0.5 L units?
lgbasallote
  • lgbasallote
what do you mean?
UnkleRhaukus
  • UnkleRhaukus
well if the millage was 7.45 does that get counted as 7.5 ?
tkhunny
  • tkhunny
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).
lgbasallote
  • lgbasallote
i don't think so
lgbasallote
  • lgbasallote
@tkhunny i don't believe in bad questions....
UnkleRhaukus
  • UnkleRhaukus
but you post so many bad questions lgba
tkhunny
  • tkhunny
If it's a legitimate question p(7.5) = 0 for any CONTINUOUS distribution.
lgbasallote
  • lgbasallote
why so?
lgbasallote
  • lgbasallote
@UnkleRhaukus no question is bad to those who see clearly
UnkleRhaukus
  • UnkleRhaukus
but you havent provided enough information to answer this question, once again
lgbasallote
  • lgbasallote
that's what you think
lgbasallote
  • lgbasallote
there are actually enough information
lgbasallote
  • lgbasallote
so much so that tkhunny is right
UnkleRhaukus
  • UnkleRhaukus
what are the increments in milage ?
lgbasallote
  • lgbasallote
you look for too much information
tkhunny
  • tkhunny
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?
lgbasallote
  • lgbasallote
hmm i don't see how that turns out to be 0 though
UnkleRhaukus
  • UnkleRhaukus
in real situation milage is a measured quantity, and it will come in incremental values
tkhunny
  • tkhunny
You didn't answer my question. Do you see how those two probabilities are calculated?
lgbasallote
  • lgbasallote
would it be because of the integral?
lgbasallote
  • lgbasallote
i did answer your question
tkhunny
  • tkhunny
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).
lgbasallote
  • lgbasallote
geometry is boring though...
lgbasallote
  • lgbasallote
by the way...i thought \[\int \limits_a^a f(x)dx\] is 0 only when f(x) is even?
lgbasallote
  • lgbasallote
or was it for odd...
tkhunny
  • tkhunny
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.
lgbasallote
  • lgbasallote
oh...yeah....
lgbasallote
  • lgbasallote
i suck in calculus
UnkleRhaukus
  • UnkleRhaukus
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 \(\text dx\)
tkhunny
  • tkhunny
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.
lgbasallote
  • lgbasallote
@UnkleRhaukus there are no increments
tkhunny
  • tkhunny
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.
lgbasallote
  • lgbasallote
class? there's no class...
tkhunny
  • tkhunny
That does make it harder to discuss things in class, then, doesn't it?!
lgbasallote
  • lgbasallote
not class as in etiquette...
UnkleRhaukus
  • UnkleRhaukus
\[\frac1n\sum{\Delta x} \longrightarrow\frac 1n\int\text dx\]
lgbasallote
  • lgbasallote
...no increments.....
UnkleRhaukus
  • UnkleRhaukus
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
lgbasallote
  • lgbasallote
yes...
lgbasallote
  • lgbasallote
0...
UnkleRhaukus
  • UnkleRhaukus
yes . bad question
lgbasallote
  • lgbasallote
you just overcomplicate things
lgbasallote
  • lgbasallote
you assume data...bad answer
UnkleRhaukus
  • UnkleRhaukus
math maps reality , reality is complicated,
lgbasallote
  • lgbasallote
that's your opinion
UnkleRhaukus
  • UnkleRhaukus
then answer to your Hypothetical question is Useless , they answer to my variation on your question is not useless
tkhunny
  • tkhunny
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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