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Instructor: Hi there.
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In in this lecture we are going to discuss
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the uniform distribution.
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For starters, we use the letter U
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to define the uniform distribution,
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followed by the range of of the values in the data set.
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Therefore, we read the following statement as
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variable X, follows a discreet uniform distribution
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ranging from three to seven.
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Events which follow the uniform distribution
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are ones where all outcomes have equal probability.
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One such event is rolling a single standard, six sided di.
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When we roll a standard six sided di,
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we have equal change of getting any value from one to six.
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The graph of the probability distribution
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would have six, equally tall bars, all reaching up to 1/6.
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Many events in gambling provide such odds,
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where each individual outcome is equally likely.
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Not only that, but many everyday situations
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follow the uniform distribution.
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If your friend offers you three, identical chocolate bars,
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the probability assigned to you choosing one of them
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also follow the uniform distribution.
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One big drawback of uniform distributions
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is that the expected value provides us
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no relevant information
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because all outcomes have the same probability.
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The expected value, which is 3.5,
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brings no predictive power.
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We can still apply the formulas from earlier
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and get a mean of 3.5 at a variance of 105 over 36.
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These values however, are completely uninterpretable
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and there is no real intuition behind what they mean.
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The main takeaway is that when an event is following
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the uniform distribution, each outcome is equally likely.
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Therefore, both the mean and the variance
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are uninterpretable and possess
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no predictive power whatsoever.
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Okay, sadly, the uniform is not the only
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discreet distribution, for which we cannot construct
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useful prediction intervals.
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In the next video, we will introduce
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the Bernoulli distribution.
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Thanks for watching.
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