M1

-終場ソ使者-

你唔明,係正常既,我估你對statistics既認識都會CE程度,
我係讀m2,不過有研究過呢個graph,俾d意見啦(我係呢方面冇接受過嚴謹既訓練)
如果你有讀AL chem,應該會見過1個probability distribution of electrons,姐係electrons圍繞住個nucleus出現既prob.(某d位置出現electrons既prob.係特別大,某d位置既prob.特別細)
又舉個例,某某地區既人既平均IQ係107,standard deviation係5,當數據夠多既話,就會plot到1條graph,呢條graph既樣就好似一條intestinal villus咁,不過係左右對稱,比較完整既,而呢條graph既function正確d既寫法係
(呢個graph係叫做normal distribution,F5 core math有教)
=standard deviation
=mean
至於只係for standard normal distribution
(core math有教,呢個interval內所佔有總數既%係68%)
而個area係用黎搵一個interval入面所佔total area既%
呢個graph係點黎,你就要多謝某某數學家/統計學家啦,係佢地好辛苦地plot出黎
上述講到個area in an interval代表該interval既%
即
d constant咁無稜兩可有咩意義呢?就係plot呢條graph既人既聰明之處,因為

如果個個constant 係其它既話,個area in interval 就唔係=1
所以個聰明人就將佢設計成area in interval =1啦
舉個例子,如下圖

紅線既=4,=35
紫線既=2,=37
所以你見到當佢既x value=,就會遇到個max. value,而就係決定佢既"粗幼程度"(大,佢會"粗"d,細,就會"幼"d)
正因為佢既area in interval =1,所以當增加,area不變,"高度"就會下降(因為"粗"左),所以個"高度"並不反映d咩架!
不過個問題係,個f(x)既面積點計呢?
放心,係唔洗要你計,對表就得,個function係比你applied番,冇乜實際用處


PS:以上內容我只係用左幾個小時既研究,有錯莫怪

-終場ソ使者-

回復 3# [H]bunbunbunbun
In fact, I don't know much about statistics, but would you mind telling me detailly on the method you used to solve the integration ?
Why double integration was used?

-終場ソ使者-

Wow! That's the most cleverest method I have never seen in solving the area under (-inf, inf)!
I have searched much in calculating the area under [a,b], but I just found nothing!
But, can we deduce a general solution by MI or other methods using distribution table?

-終場ソ使者-

琴晚睇番條數,突然俾我諗到1個方法
Let ,
=>, .
Therefore, we have

.
Using integration by parts, we have

.
Therefore, we have
.