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  • In statistics, when we use the term distribution, we usually mean a probability distribution.

  • Good examples are the Normal distribution, the Binomial distribution, and the Uniform

  • distribution.

  • Alright.

  • Let’s start with a definition!

  • A distribution is a function that shows the possible values for a variable and how often

  • they occur.

  • Think about a die.

  • It has six sides, numbered from 1 to 6.

  • We roll the die.

  • What is the probability of getting 1?

  • It is one out of six, so one-sixth, right?

  • What is the probability of getting 2?

  • Once again - one-sixth.

  • The same holds for 3, 4, 5 and 6.

  • Now.

  • What is the probability of getting a 7?

  • It is impossible to get a 7 when rolling a die.

  • Therefore, the probability is 0.

  • The distribution of an event consists not only of the input values that can be observed,

  • but is made up of all possible values.

  • So, the distribution of the event - rolling a die - will be given by the following table.

  • The probability of getting one is 0.17, the probability of getting 2 is 0.17, and so on...

  • you are sure that you have exhausted all possible values when the sum of probabilities is equal

  • to 1% or 100%.

  • For all other values, the probability of occurrence is 0.

  • Each probability distribution is associated with a graph describing the likelihood of

  • occurrence of every event.

  • Here’s the graph for our example.

  • This type of distribution is called a uniform distribution.

  • It is crucial to understand that the distribution is defined by the underlying probabilities

  • and not the graph.

  • The graph is just a visual representation.

  • Alright.

  • Now think about rolling two dice.

  • What are the possibilities?

  • One and one, two and one, one and two, and so on.

  • Here’s a table with all the possible combinations.

  • We are interested in the sum of the two dice.

  • So, what’s the probability of getting a sum of 1?

  • It’s 0, as this event is impossible.

  • What’s the probability of getting a sum of 2?

  • There is only one combination that would give us a sum of 2 – when both dice are equal

  • to 1.

  • So, 1 out of 36 total outcomes, or 0.03.

  • Similarly, the probability of getting a sum of 3 is given by the number of combinations

  • that give a sum of three divided by 36.

  • Therefore, 2 divided by 36, or 0.06.

  • We continue this way until we have the full probability distribution.

  • Let’s see the graph associated with it.

  • Alright.

  • So, looking at it we understand that when rolling two dice, the probability of getting

  • a 7 is the highest.

  • We can also compare different outcomes such as: the probability of getting a 10 and the

  • probability of getting a 5.

  • It’s evident that it’s less likely that well get a 10.

  • Great!

  • The examples that we saw here were of discrete variables.

  • Next, we will focus on continuous distributions, as they are more common in inferences.

  • In the next few lessons, well examine some of the main types of continuous distributions,

  • starting with the Normal distribution.

In statistics, when we use the term distribution, we usually mean a probability distribution.

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B1 中級

ディストリビューションとは? (What is a distribution?)

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    林宜悉 に公開 2021 年 01 月 14 日
動画の中の単語