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Canolrif Dosraniad Di-or

F(x). 1. x. 0. a. b. Canolrif Dosraniad Di-or. The Median of a Continuous Distribution. I ddarganfod canolrif hapnewidyn gyda dosraniad di-dor, rydym yn defnyddio’r ffwythiant dosraniad cronnus F(x).

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Canolrif Dosraniad Di-or

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  1. F(x) 1 x 0 a b Canolrif Dosraniad Di-or The Median of a Continuous Distribution I ddarganfod canolrif hapnewidyn gyda dosraniad di-dor, rydym yn defnyddio’r ffwythiant dosraniad cronnus F(x). To calculate the median of a continuous distribution, we must use the cumulative distribution function F(x). Mae’r tebygolrwydd fod gan X werth llai na’r canolrif yn 0.5. The probability that X has a lower value than the median is 0.5. P(X ≤ x0.5) = F(x0.5) = 0.5 0.5 x0.5

  2. Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan The continuous random variable X is distributed with cumulative distribution function F where F(x) = 0 ar gyfer/for x < 0 F(x) = ar gyfer/for 0 ≤ x ≤ 4 F(x) = 1 ar gyfer/for x > 4 Darganfyddwch y canolrif Find the median F(x0.5) = 0.5

  3. F(x) F(x) 1 1 x x 0 0 a a b b 0.75 0.25 x0.25 x0.75 Mae’n bosib hefyd defnyddio’r ffwythiant dosraniad cronnus F(x) i ddarganfod amrediad rhyng-chwartel ac amrediad rhyng-ganraddol y dosraniad. It is also possible to use the cumulative distribution function F(x) in order to calculate the inter-quartile range and the inter-percentile range of the distribution. Yr Amrediad rhyng-chwartel – The inter-quartile range Mae’r tebygolrwydd fod gan X werth llai na’r chwartel isaf yn 0.25. Mae’r tebygolrwydd fod gan X werth llai na’r chwartel uchaf yn 0.75. The probability that X has a lower value than the lower quartile is 0.25. The probability that X has a lower value than the upper quartile is 0.75. P(X ≤ x0.25) = F(x0.25) = 0.25 P(X ≤ x0.75) = F(x0.75) = 0.75

  4. Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan The continuous random variable X is distributed with cumulative distribution function F where F(x) = 0 ar gyfer/for x < 0 F(x) = ar gyfer/for 0 ≤ x ≤ 4 F(x) = 1 ar gyfer/for x > 4 Darganfyddwch yr amrediad rhyng-chwartel Calculate the inter-quartile range. F(x0.75) - F(x0.25) F(x0.75) = F(x0.25) = Amrediad rhyng-chwartel = 3.63 – 2.52 = 1.11 Inter-quartile range =

  5. Yr Amrediad rhyng-ganraddol - The inter-percentile range Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan The continuous random variable X is distributed with cumulative distribution function F where F(x) = 0 ar gyfer/for x < 0 F(x) = ar gyfer/for 0 ≤ x ≤ 4 F(x) = 1 ar gyfer/for x > 4 Darganfyddwch yr amrediad rhyng-ganraddol 10-90 Calculate the inter-percentile range 10-90 F(x0.9) - F(x0.1) F(x0.1) = F(x0.9) = Amrediad rhyng-ganraddol 10-90 = 3.86 – 1.86 = 2 The inter-percentile range 10-90 =

  6. Ymarfer Canraddau/Percentile Exercise Gwaith Cartref/Homework 13

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