## 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

1. hartnn Group Title

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 Group Title

hmmm....

3. UnkleRhaukus Group Title

uniform probability distribution eh,

4. lgbasallote Group Title

^?

5. UnkleRhaukus Group Title

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

6. lgbasallote Group Title

what do you mean?

7. UnkleRhaukus Group Title

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

8. tkhunny Group Title

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 Group Title

i don't think so

10. lgbasallote Group Title

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

11. UnkleRhaukus Group Title

but you post so many bad questions lgba

12. tkhunny Group Title

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

13. lgbasallote Group Title

why so?

14. lgbasallote Group Title

@UnkleRhaukus no question is bad to those who see clearly

15. UnkleRhaukus Group Title

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

16. lgbasallote Group Title

that's what you think

17. lgbasallote Group Title

there are actually enough information

18. lgbasallote Group Title

so much so that tkhunny is right

19. UnkleRhaukus Group Title

what are the increments in milage ?

20. lgbasallote Group Title

you look for too much information

21. tkhunny Group Title

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 Group Title

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

23. UnkleRhaukus Group Title

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

24. tkhunny Group Title

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

25. lgbasallote Group Title

would it be because of the integral?

26. lgbasallote Group Title

27. tkhunny Group Title

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 Group Title

geometry is boring though...

29. lgbasallote Group Title

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

30. lgbasallote Group Title

or was it for odd...

31. tkhunny Group Title

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 Group Title

oh...yeah....

33. lgbasallote Group Title

i suck in calculus

34. UnkleRhaukus Group Title

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 Group Title

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 Group Title

@UnkleRhaukus there are no increments

37. tkhunny Group Title

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 Group Title

class? there's no class...

39. tkhunny Group Title

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

40. lgbasallote Group Title

not class as in etiquette...

41. UnkleRhaukus Group Title

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

42. lgbasallote Group Title

...no increments.....

43. UnkleRhaukus Group Title

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 Group Title

yes...

45. lgbasallote Group Title

0...

46. UnkleRhaukus Group Title

yes . bad question

47. lgbasallote Group Title

you just overcomplicate things

48. lgbasallote Group Title

49. UnkleRhaukus Group Title

math maps reality , reality is complicated,

50. lgbasallote Group Title