docs: update education/statistics/random-variable
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title: 隨機變數 (Random Variable)
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description:
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published: true
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date: 2025-12-28T19:30:53.863Z
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date: 2025-12-28T19:33:09.392Z
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tags:
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editor: ckeditor
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dateCreated: 2025-12-28T16:41:51.938Z
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-->
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<h2>General</h2>
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<h3>Symmetric</h3>
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<p>If there is a point that,</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p>Then,</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p>Is the expectation of this random variable, equal to the point of symmetry.</p>
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<p> </p>
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<h3>Median and Quantiles</h3>
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<p>The middle value of the random variable.<br>For median, set <strong>p</strong> to <strong>0.5</strong>.</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p> </p>
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<h3>Variance</h3>
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<p>A positive quantity that measures the spread of the distribution of the random variable about its mean value.<br>Larger values of the variance indicate that the distribution is more spread out.</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p> </p>
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<h2>Discrete</h2>
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<h3>Probability Mass Function (PMF)</h3>
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<p>A set of probability value <strong>p<sub>i</sub></strong> assigned to each of the values taken by the discrete random variables <strong>x<sub>i</sub></strong>.</p>
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<p>satisfying </p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p> </p>
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<h2>Continuous</h2>
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<h3><strong>Joint Cumulative</strong></h3>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<h3>Marginal Probability Distributions</h3>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<h2>Contin</h2>
|
||||
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMgAAAA7CAMAAAAJgDUbAAAAAXNSR0IArs4c6QAAAMNQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZma2ZpDbZrbbZrb/kDoAkDo6kGY6kGZmkGaQkLbbkLb/kNu2kNvbkNv/tmYAtmY6tmZmtpA6tpBmtra2ttvbttv/tv+2tv//25A625Bm25CQ27Zm27aQ27a229uQ29vb2/+22//b2////7Zm/9uQ/9u2/9vb//+2///bge4KawAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAE7ElEQVRoQ+1afVvTMBBfx1CLL4yKKGwORNb5husARWln8/0/lblLsqZt2t7ROB6fh/yhkP56ubv87nK5Mhg8jkcP/H8eSAPnGM5dprDA2/ZFHAQ7y/Ki4nPgNmTAAm/ZkjwKgmfVNeMGQ1jgLRsyyMIgmFQWTRsM4YG3bUkS1JiU7TljRGrGAm/ZEjENgt074qIsMFGmNxgw/4AqjQWmCvWFg7RaDZNG2SywLw2pciTzqzm4+VUWmKqBJxwwv5aDm2SzwB0Krmf77dGZvPzGspHFfBa4VY1076RLzfXhuAtSei6Z33R21OWwwKXXwQc4ME2mlMjMI3IiwqVYzGeBS5ZkEZiQR0BkooqNp7N7p1jMZ4HLhoQYizEkyYTGATElhy8u5SpVGtnJAttSLDaJKfEYJhq8WYbFfBbYssRSSvFLjkUwWg7E1Nqf63Aos4AMKHoo2d6SRTrRR0COFrD4Eg7nYhEMa6cs7sL6NVZyWaiieHUifxLvreoue/cbd0sjDFBF8mY05wDJfBprYfk2cCJVOzm9FNPaKauylnJXoZ+YPl1UbMadS9X7liGNXC8/SEP6+T5oBWfhS6lD/VqTQlGXKF9a+sXBuKIixlIdSDOkRNOuV9rBCZ4QdUPsuLUMqWdYeJgfqasre0cSeg0MbG07p2JgD1JL65ggnUpk2wT7ID+snYzwMNF0szIdKUZSerkFh3JbclepP1NnhjUK3dEqk1oWF/WjIt79aejGTL95xAiQDrAiAzArxo2TMY7eTUrmGwVlKMQ7S/S//F/bnQwhymBwD8SmhoMzWDrAcr/uZC9GqpZHaIG6O8NVxtoktT/J8Bg2D/61DSn4xCxRPAaI1Gc0C4IR6J49R7+mzgOqXjRibOFIDbHyyPzkdGl1ss7nlte6wBYZtAWJO6KqZbzeP3DAK20Rs4z3GSClsjZGC8S0IcX9WZQuVom6nsSTG2PHinmxiik3A7NHneCCMtKCm/NNpJC4gUXDmNrVqYj0GiCQnDA+YCzwzGbGK9HgOiwL6cWiTDAMsF5LHYf/fPgNEIe6a+Zt9b4W1znfcgaxwKhRD8rzLHIESKmUKEljgXl69EW7ON9YSbHAfTXjve8KkPVhQ2nLAvP06I2WV1bXcB9gLHBv1VgC7ALfNsjZ02aBWWr0BkODyjlchrDAvVV7FPDogYf3AKuU21K55Nsr4pYjkYfmSCZhVV9AjiwcLcXMaj2sZ0P5yJ423QNdl29ehdcVGuv10jxJCR8guFdCdSjOfkWTTxdnutIW1y/wVlaehu4BgLNz6GMW3+ENujrvQ0GqDOgL6DI3Vu1muFnn0f6lkaCn4Ve4e5tu1UR1BsARFjoL9Tx1fW84q7NhRzL4+INaxJouugdw/15sWucFujzvTUuCINUXwCB5A02bopu7nmGDTU3jsLsH8UEKT1PzDUKjB3qesLJfCPYFgC2rj0ffo8nV3PSgcJnbYhp+xT6N5mHyRDWX46KwxBxn5v2qSZAGeQZ0i0eXqiWNXBOnb2EcF9MgCo8cbYjukYgp2GbQuEXkv54gaNcHgi4WP77CqHymt4NIf7XI4buTjdbzfTTw86508VXlb+mM4KJ7sJpfj9Ws/pykIcW8H2X6SBExfIF0DKt7IBMCNpshJOwWjzXfR4UHedeK9QdZ39eizX9k52uFrci5F5X+AuQejmebI57qAAAAAElFTkSuQmCC"></figure>
|
||||
<h2>uous</h2>
|
||||
<h3>Probability Density Function (PDF)</h3>
|
||||
<p>Probabilistic properties of a continuous random variable.</p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
@@ -41,27 +66,16 @@ dateCreated: 2025-12-28T16:41:51.938Z
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<figure class="image"><img src="data:image/png;base64,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 truncated
|
||||
<p> </p>
|
||||
<h3>Symmetric</h3>
|
||||
<p>If there is a point that,</p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p>Then,</p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p>Is the expectation of this random variable, equal to the point of symmetry.</p>
|
||||
<p> </p>
|
||||
<h3>Median and Quantiles</h3>
|
||||
<p>The middle value of the random variable.<br>For median, set <strong>p</strong> to <strong>0.5</strong>.</p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<h3>Variance</h3>
|
||||
<p>A positive quantity that measures the spread of the distribution of the random variable about its mean value.<br>Larger values of the variance indicate that the distribution is more spread out.</p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<h3>Jointly Distributed</h3>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p>satisfying </p>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<h3><strong>Joint Cumulative</strong></h3>
|
||||
<figure class="image"><img src="data:image/png;base64,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 truncated
|
||||
<p> </p>
|
||||
<h3>Marginal Probability Distributions</h3>
|
||||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
Reference in new issue
Block a user