Introduction to the Continuous Uniform Distribution

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A brief introduction to the (continuous) uniform distribution. I discuss its pdf, median, mean, and variance. I also work through an example of finding a probability and a percentile. I don't do any integration in this video.

For those using R, here is the R code to find the probabilities for the examples in this video:

P(X greater than 230) where X is U(200,250):
1-punif(230,200,250)
[1] 0.4
(punif yields the area to the *left*, and here we need the area to the *right*)

20th percentile of a U(200,250) distribution:
qunif(.2,200,250)
[1] 210
  1. jbstatistics
  2. uniform distribution
  3. continuous uniform
  4. mean
  5. median
  6. variance
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Some sources have the boundaries included, some not. Unless we're getting very technical, it doesn't matter whether we say f(x) = 1/(d-c) for c < x < d, or c < = x < = d. The cumulative distribution function F(x) = P(X <=x ) will be 0 for x < = c in either case, and F(x) = 1 for x greater or equal to d in either case as well. Whether the boundaries are included or not doesn't change anything, other than very technical details that are far beyond my treatment of this topic.

jbstatistics
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great video man i've been missing my lectures this is helpful

mistathugisolation
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Hi I have a question for the discussion at 1:45. I thaught that f(x)=0 if x is greater than or equal to c. and f(x)=1 if x is greater than or equal to d. So I thaught that f(x) can only to equal to 1/d-c if x is greater than c (not equal to) and less than d (not equal to). Have I misunderstood this?

mickysahi