Finding a Probability for a Uniform Distribution

# Finding a Probability for a Uniform Distribution

0:00:00.000,0:00:09.000 This is a video on the uniform distribution. The question states: The waiting time for 0:00:09.000,0:00:19.066 the train that leaves every 30 minutes is
uniformly distributed from 0 to 30 minutes. Find the 0:00:19.066,0:00:28.033 probability that a person arriving at a random time will wait between 10 and 15 minutes. 0:00:28.033,0:00:37.000 Let’s start out by drawing a diagram. We have a uniform distribution. We always know 0:00:37.000,0:00:47.033 when we have a uniform distribution we get
a rectangle. The f(x) curve is horizontal. 0:00:47.033,0:00:53.066 We are going from 0 to 30, in terms of the
wait times. For the area of the rectangle to 0:00:53.066,0:01:04.033 equal 1, the height must be 1/30, because
1/30 times 30 equals 1. We want to find the 0:01:04.033,0:01:12.000 probability that the wait time is between
10 and 15 minutes. So we want the part of the 0:01:12.000,0:01:21.033 rectangle between 10 and 15. We want to find out its area. In particular, the probability that 0:01:21.033,0:01:29.000 the wait time x is between 10 and 15 is the
area of the rectangle which is the length of 0:01:29.000,0:01:35.000 the base, and that we can calculate by taking
15 and subtracting 10. We see that 0:01:35.000,0:01:47.000 that base is of lenght 5. Times the height. The height is 1/30. Then 15 – 10=5. Divide by 30 0:01:47.000,0:01:55.033 to get 5/30. We can reduce and say the probability is 1/6. Now I can state my conclusion. 0:01:55.033,0:02:04.066 In conclusion, the probability that a person arriving at a random time will wait between 0:02:04.066 10 and 15 minutes is 1/6. I am done with the problem.

## 23 Replies to “Finding a Probability for a Uniform Distribution”

1. Dennis Ancheta says:

Great explanation! It was very easy to follow

2. SwiftlyTilt says:

Dude you're awesome

Thank you for the help, even if you did read it like a creeper.

4. Angel Valle says:

Great video! Thanks a bunch!!

5. Samantha Bernard says:

nice simple example π

6. Awad Albaqawi says:

you rock !!

7. doglover04005 says:

Thanks for posting this; it helped me a lot with some homework! π

8. Doaa M says:

thanks for simple example Β

9. Jutzy De La Cruz says:

thank you !!

10. Juan says:

thank you, good example

11. mikeyuncensored says:

i understand the gist of it, but where does the 1/30 come from. Does that just mean 1 out of 30 minutes?

12. Karl Lrak says:

thank you so much π i hope you're still active in this account. You have helped so much people inclucing me π

13. nicewarlock says:

This was a life saver π

14. Tina Yip says:

thanks! this helped me a lot.

15. Derek Halder says:

I was wondering if you help me with uniform
distribution from one to 53 (spread of 52)

P(12 < x|x < 28)

16. lolzomgz1337 says:

If, for instance, I wanted to calculate the probability that three people would have to wait between 10 and 15 minutes, provided that they are totally independent of each other, would I literally just cube the answer here, or is there something else going on?

17. Katie says:

thank you so much, you explained it perfectly!

18. Anglo Eternal says:

that voice

19. Keotshepile Mandona says:

this is exactly what ive been looking for

20. OEFVET says:

Found your video to clarify a jumbled mess regarding uniform distributions, excellent explanation, and the graphical representation was a huge plus! I hope you make future how-to videos using technology (Ti-84, Casio Fx-CG50) for statistics/business statistics students.

21. Daniel Rosen says:

Thanks for your videos on Probability. Theyβre very helpful. Going to watch the one on Binomial Probabilities. Thanks again.

22. Tumenbayar Munkhjargal says: