A point chosen at random

👨🏻‍🏫 學術台數學

[匿名]

2013-05-06 4:01 pm

A point is chosen uniformly at random from the circumference of a circle of diameter 1. Let X be the length of the chord joining the random point to an arbitrary fixed point on the circumference. Find a) cdf of X b) E(X) c) Var(X).

更新1:

How do you get the length of x?

更新2:

And how do you get the range of x?

回答 (1)

用戶9112

2013-05-07 4:55 am

✔ 最佳答案

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圖片參考：http://imgcld.yimg.com/8/n/HA05107138/o/20130506205231.jpg

2013-05-06 20:56:27 補充：
Var(X) should be 2-16/PI^2

2013-05-06 22:27:27 補充：
Var = 2 - 16 / Pi^2

2013-05-07 19:35:51 補充：
I mis-read the question and take the radius = 1 instead of the diameter.
Updated solution:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1072_zps40854eb3.png

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收錄日期: 2021-04-24 10:18:10
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