diff --git a/education/statistics/random-variable.html b/education/statistics/random-variable.html index 6c689db..1f945b3 100644 --- a/education/statistics/random-variable.html +++ b/education/statistics/random-variable.html @@ -2,7 +2,7 @@ title: 隨機變數 (Random Variable) description: published: true -date: 2025-12-28T19:45:37.395Z +date: 2025-12-28T19:47:43.526Z tags: editor: ckeditor dateCreated: 2025-12-28T16:41:51.938Z @@ -24,6 +24,13 @@ dateCreated: 2025-12-28T16:41:51.938Z
A positive quantity that measures the spread of the distribution of the random variable about its mean value.
Larger values of the variance indicate that the distribution is more spread out.
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Independent random variables have a covariance of zero.
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| Continuous | ||
| Probability A set of probability value pi assigned to each of the values taken by the discrete random variables xi. |
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+ Probability +A set of probability value pi assigned to each of the values taken by the discrete random variables xi. + |
Probability Mass Function (PMF) |
| Cumulative A set of probability value pi assigned to each of the values taken by the discrete random variables xi. |
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+ Cumulative +A set of probability value pi assigned to each of the values taken by the discrete random variables xi. + |
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| Marginal Probability Obtained by summing or integrating the joint probability distribution over the values of the other random variable. |
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+ Marginal Probability +Obtained by summing or integrating the joint probability distribution over the values of the other random variable. + |
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@@ -97,7 +113,10 @@ dateCreated: 2025-12-28T16:41:51.938Z
| Conditional Probability The probabilistic properties of the random variable X under the knowledge provided by the value of Y. |
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+ Conditional Probability +The probabilistic properties of the random variable X under the knowledge provided by the value of Y. + |
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@@ -105,6 +124,20 @@ dateCreated: 2025-12-28T16:41:51.938Z
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+ Independence +Two random variables X and Y are said to be independent if: + |
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+ for all values i of X and j of Y. + |
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+ for all X and Y. + |
+