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

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

3. Mae’n bosib hefyd defnyddio’r ffwythiant dosraniad cronnus F(x) i ddarganfod amrediad rhyng-chwartel ac amrediad rhyng-ganraddol y dosraniad. Mae’r tebygolrwydd fod gan X werth llai na’r chwartel isaf yn 0.25. P(X ≤ x 0.25 ) = F(x 0.25 ) = 0.25 a b F(x) x 0 1 0.25 x 0.25 Mae’r tebygolrwydd fod gan X werth llai na’r chwartel uchaf yn 0.75. P(X ≤ x 0.75 ) = F(x 0.75 ) = 0.75 a b F(x) x 0 1 0.75 x 0.75 Yr Amrediad rhyng-chwartel – The inter-quartile range 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. 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.

4. F(x) = 0ar gyfer/ for x < 0 F(x) = ar gyfer/ for 0 ≤ x ≤ 4 F(x) = 1ar gyfer/ for x > 4 Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan Darganfyddwch yr amrediad rhyng-chwartel F(x 0.75 ) - F(x 0.25 ) F(x 0.75 ) =F(x 0.25 ) = Amrediad rhyng-chwartel = 3.63 – 2.52 = 1.11 The continuous random variable X is distributed with cumulative distribution function F where Calculate the inter-quartile range. Inter-quartile range =

5. Yr Amrediad rhyng-ganraddol - The inter-percentile range Darganfyddwch yr amrediad rhyng-ganraddol 10-90 F(x 0.9 ) - F(x 0.1 ) F(x 0.9 ) = F(x 0.1 ) = Amrediad rhyng-ganraddol 10-90 = 3.86 – 1.86 = 2 F(x) = 0ar gyfer/for x < 0 F(x) = ar gyfer/for 0 ≤ x ≤ 4 F(x) = 1ar gyfer/for x > 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 Calculate the inter-percentile range 10-90 The inter-percentile range 10-90 =

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