Question

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?

Answer 1

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)

Answer 2

hmmm....

Answer 3

uniform probability distribution eh,

Answer 4

^?

Answer 5

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

Answer 6

what do you mean?

Answer 7

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

Answer 8

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).

Answer 9

i don't think so

Answer 10

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

Answer 11

but you post so many bad questions lgba

Answer 12

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

Answer 13

why so?

Answer 14

@UnkleRhaukus no question is bad to those who see clearly

Answer 15

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

Answer 16

that's what you think

Answer 17

there are actually enough information

Answer 18

so much so that tkhunny is right

Answer 19

what are the increments in milage ?

Answer 20

you look for too much information

Answer 21

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?

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

would it be because of the integral?

Answer 26

i did answer your question

Answer 27

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).

Answer 28

geometry is boring though...

Answer 29

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

Answer 30

or was it for odd...

Answer 31

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.

Answer 32

oh...yeah....

Answer 33

i suck in calculus

Answer 34

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 \(\text dx\)

Answer 35

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.

Answer 36

@UnkleRhaukus there are no increments

Answer 37

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.

Answer 38

class? there's no class...

Answer 39

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

Answer 40

not class as in etiquette...

Answer 41

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

Answer 42

...no increments.....

Answer 43

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

Answer 44

yes...

Answer 45

0...

Answer 46

yes .
bad question

Answer 47

you just overcomplicate things

Answer 48

you assume data...bad answer

Answer 49

math maps reality , reality is complicated,

Answer 50

that's your opinion

Answer 51

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

Answer 52

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!