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  • Welcome back!

  • In this video we will talk about discrete distributions and their characteristics.

  • Let’s get started!

  • Earlier in the course we mentioned that events with discrete distributions have finitely

  • many distinct outcomes.

  • Therefore, we can express the entire probability distribution with either a table, a graph

  • or a formula.

  • To do so we need to ensure that every unique outcome has a probability assigned to it.

  • Imagine you are playing darts.

  • Each distinct outcome has some probability assigned to it based on how big its associated

  • interval is.

  • Since we have finitely many possible outcomes, we are dealing with a discrete distribution.

  • Great!

  • In probability, we are often more interested in the likelihood of an interval than of an

  • individual value.

  • With discrete distributions, we can simply add up the probabilities for all the values

  • that fall within that range.

  • Recall the example where we drew a card 20 times.

  • Suppose we want to know the probability of drawing 3 spades or fewer.

  • We would first calculate the probability of getting 0, 1, 2 or 3 spades and then add them

  • up to find the probability of drawing 3 spades or fewer.

  • One peculiarity of discrete events is that theThe probability of Y being less than

  • or equal to y equals the probability of Y being less than y plus 1”.

  • In our last example, that would mean getting 3 spades or fewer is the same as getting fewer

  • than 4 spades.

  • Alright!

  • Now that you have an idea about discrete distributions, we can start exploring each type in more detail.

  • In the next video we are going to examine the Uniform Distribution.

  • Thanks for watching!

  • 4.4 Uniform Distribution

  • Hey, there!

  • In this lecture we are going to discuss the uniform distribution.

  • For starters, we use the letter U to define a uniform distribution, followed by the range

  • of the values in the dataset.

  • Therefore, we read the following statement asVariable “X” follows a discrete

  • uniform distribution ranging from 3 to 7”.

  • Events which follow the uniform distribution, are ones where all outcomes have equal probability.

  • One such event is rolling a single standard six-sided die.

  • When we roll a standard 6-sided die, we have equal chance of getting any value from 1 to

  • 6.

  • The graph of the probability distribution would have 6 equally tall bars, all reaching

  • up to one sixth.

  • Many events in gambling provide such odds, where each individual outcome is equally likely.

  • Not only that, but many everyday situations follow the Uniform distribution.

  • If your friend offers you 3 identical chocolate bars, the probabilities assigned to you choosing

  • one of them also follow the Uniform distribution.

  • One big drawback of uniform distributions is that the expected value provides us no

  • relevant information.

  • Because all outcomes have the same probability, the expected value, which is 3.5, brings no

  • predictive power.

  • We can still apply the formulas from earlier and get a mean of 3.5 and a variance of 105

  • over 36.

  • These values, however, are completely uninterpretable and there is no real intuition behind what

  • they mean.

  • The main takeaway is that when an event is following the Uniform distribution, each outcome

  • is equally likely.

  • Therefore, both the mean and the variance are uninterpretable and possess no predictive

  • power whatsoever.

  • Okay!

  • Sadly, the Uniform is not the only discrete distribution, for which we cannot construct

  • useful prediction intervals.

  • In the next video we will introduce the Bernoulli Distribution.

Welcome back!


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B1 中級

離散均勻分佈簡介 (Introduction to Discrete Uniform Distribution)

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    林宜悉 發佈於 2021 年 01 月 14 日