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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

• 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!

B1 中級

# 離散一様分布入門 (Introduction to Discrete Uniform Distribution)

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林宜悉 に公開 2021 年 01 月 14 日