1. Ffwythiant Dosraniad Cronnus F(x)
4.3
Ffwythiant Dosraniad Cronnus F(x)
Cumulative Distribution Function F(x)
Mae’n bosib hefyd defnyddio Ffwythiant Dosraniad Cronnus ar gyfer darganfod tebygolrwydd.
It is also possible to use the cumulative probability function to calculate probability. a b
F(x) x 1
F(x) = P(X ≤ x) ar gyfer pob x.
F(x) = P(X ≤ x) for all x.
Mae’r tebygolrwydd yn 0 ar gyfer unrhyw werth o dan a ac yn 1 ar gyfer unrhyw werth dros b.
The probability is 0 for any value under a, and 1 for any value over b.
F(x) = 0, ar gyfer/for x < a
F(b) = 1, ar gyfer/for x > b

2. I ddarganfod P(x ≤ c) P(x ≤ c) = F(c) I ddarganfod P(c ≤ x ≤ d)
To find P(x ≤ c)
F(x)
P(x ≤ c) = F(c) c x a b a b
F(x) x
I ddarganfod P(c ≤ x ≤ d)
To find P(c ≤ x ≤ d)
P(c ≤ x ≤ d) = F(d) – F(c) d c

3. F(x) = 0 ar gyfer/for x < 1 F(x) = ar gyfer/for 1 ≤ x ≤ 3
Enghraifft - Example
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan
F(x) = 0 ar gyfer/for x < 1
F(x) = ar gyfer/for 1 ≤ x ≤ 3
F(x) = 1 ar gyfer/for x > 3
Darganfyddwch
Find
P(X < 2)
P(X > 1½)
P(1½ < X ≤ 2½)
The continuous random variable X is distributed with cumulative distribution function F where

4. P(X < 2) = F(2) =
b) P(X > 1½) = 1 – F(1½) =
c) P(1½ < X ≤ 2½) = F(2½) - F(1½)

5. Newid Ffwythiant Dwysedd Tebygolrwydd f(x) i Ffwythiant Dosraniad Cronnus F(x)
Change Probability Density Function f(x) to Cumulative Distribution Function F(x)
f(x)  F(x)
Gan fod F(x) = P(X ≤x), i newid o f(x) i F(x) rydym yn integru
rhwng y terfan isaf ac x.
Since F(x) = P(X ≤x), in order to change f(x) to F(x) we must integrate between the lower limit and x.
ar gyfer/for 0 ≤ x ≤ 4

6. F(x) = 0 ar gyfer/for x < 0 F(x) = ar gyfer/for 0 ≤ x ≤ 4
Ymarfer Ffwythiant Dosraniad Cronnus
Cumulative Distribution Function Exercise