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?

- lgbasallote

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- 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

hmmm....

- UnkleRhaukus

uniform probability distribution eh,

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- lgbasallote

^?

- UnkleRhaukus

and i suppose that , measurements are in 0.l L, or are they in 0.5 L units?

- lgbasallote

what do you mean?

- UnkleRhaukus

well if the millage was 7.45 does that get counted as 7.5 ?

- 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

i don't think so

- lgbasallote

@tkhunny i don't believe in bad questions....

- UnkleRhaukus

but you post so many bad questions lgba

- tkhunny

If it's a legitimate question p(7.5) = 0 for any CONTINUOUS distribution.

- lgbasallote

why so?

- lgbasallote

@UnkleRhaukus no question is bad to those who see clearly

- UnkleRhaukus

but you havent provided enough information to answer this question, once again

- lgbasallote

that's what you think

- lgbasallote

there are actually enough information

- lgbasallote

so much so that tkhunny is right

- UnkleRhaukus

what are the increments in milage ?

- lgbasallote

you look for too much information

- 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

hmm i don't see how that turns out to be 0 though

- UnkleRhaukus

in real situation milage is a measured quantity, and it will come in incremental values

- tkhunny

You didn't answer my question. Do you see how those two probabilities are calculated?

- lgbasallote

would it be because of the integral?

- lgbasallote

i did answer your question

- 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

geometry is boring though...

- lgbasallote

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

- lgbasallote

or was it for odd...

- 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

oh...yeah....

- lgbasallote

i suck in calculus

- 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

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

@UnkleRhaukus there are no increments

- 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

class? there's no class...

- tkhunny

That does make it harder to discuss things in class, then, doesn't it?!

- lgbasallote

not class as in etiquette...

- UnkleRhaukus

\[\frac1n\sum{\Delta x} \longrightarrow\frac 1n\int\text dx\]

- lgbasallote

...no increments.....

- 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

yes...

- lgbasallote

0...

- UnkleRhaukus

yes .
bad question

- lgbasallote

you just overcomplicate things

- lgbasallote

you assume data...bad answer

- UnkleRhaukus

math maps reality , reality is complicated,

- lgbasallote

that's your opinion

- UnkleRhaukus

then answer to your Hypothetical question is Useless ,
they answer to my variation on your question is not useless

- 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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