HKGC 2019-10-29 12:34 AM

Choose a number X uniformly ar random from the interval [0,10]. Then, define Y as follow: if the number X is <= 6 , then ley Y equal X divided by 3, if the number X is > 6, then Y is equal to X multiple by 2, compute and plot the CDF.

[[i] 本帖最後由 HKGC 於 2019-10-29 03:14 AM 編輯 [/i]]

HKGC 2019-10-29 08:15 AM

hkpal 2019-10-29 03:03 PM

[quote]原帖由 [i]HKGC[/i] 於 2019-10-29 12:34 AM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=509164582&ptid=28638403][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
Choose a number X uniformly ar random from the interval [0,10]. [/quote]
For any x in [0,10], PDF f(x) = 1/10.
What is the total probability for all x in [0,6] ? say A.
What is the total probability for all x in [6,10] ? i.e. 1-A.

[quote]Then, define Y as follow: if the number X is <= 6 , then ley Y equal X divided by 3, if the number X is > 6, then Y is equal to X multiple by 2, [/quote]

x in [0,6]  <--y=x/3-->   y in [0,2]  Total probability A
x in [6,10] <--y=2x-->   y in [12,20] Total probability 1-A

[quote]compute and plot the CDF.[/quote]
Total probability for y in [0,2] is A.
Total probability for y in [2,12] is zero.
Total probability for y in [12,20] is 1-A.
You should then be able to find PDF f(y), and subsequently CDF F(y) for y from 0 to 20.

[quote]係咪conditional CDF??? 應該係DISCRETE 但完全唔識 [/quote]
[url]https://en.wikipedia.org/wiki/Cumulative_density_function[/url]