正态分布得概率密度函数得推导An inte ｒ e ｓ ting que ｓｔ io ｎ ｗ as posed in ａ Stati ｓｔ ics as ｓ i ｇ nmen ｔ w ｈ ich was to s ｈ o ｗ t ｈ a ｔ the standard no ｒ m ａ l di ｓ tr ｉ butio ｎ wa ｓ va ｌｉ d - ie ｔ he ｉ nte ｇｒ al ｆｒ o ｍ negat ｉ ve infin ｉｔｙ to i ｎｆｉ nity e ｑ uat ｅｄ to o ｎｅ and in ｄｏ ing so sh ｏ wed the derivati ｏ n ｏ f th ｅ part of the n ｏ rma ｌ pd ｆ 、A frien ｄ of ｍ ine and Ｉ deci ｄｅ d to try ｔｏ d ｅｒｉｖ e the ｎ o ｒ mal ｐｄ f and the ｔ hin ｋ ing w ｅ nt along the lines ｏ f t ｈ e centra ｌ ｌ i ｍ i ｔ the ｏ rem whic ｈ s ｔate ｓ that t ｈｅ m ｅ an ｏ f a ｎ y ｐ ro ｂ ability dis ｔ ributio ｎ ｂ ees nor ｍａ l a ｓ the nｕ mber of ｔ ria ｌｓ incr ｅ ases、The derivatio ｎ of this is well known、 but we ask ｅ d ｏｕ rs ｅｌ ves ｈｏ w ｔｈｅ ｎo ｒｍ al distribution was ｆｉ rs ｔ a ｃ hi ｅ ved、 Ther ｅ ｉ s another 'norma ｌ' derｉｖａ t ｉ on
