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 whi ｃ h i ｓ the b ｉ nomial app ｒｏｘｉｍ ati ｏ n and it ｉ s thr ｏ ugh tｈｉ s d ｉｒ ect ｉｏ n th ａ t ｗ e wo ｎ d ｅ r ｅ d h ｏ w to de ｒｉｖ e the ｎｏ rm ａ l ｄｉstri ｂ ut ｉｏ n ｆ r ｏ m the bi ｎ o ｍ ial a ｓ n get ｓ large、So t ｈｅ general a ｐ proach w ｅ wil ｌ ｔａ ke i ｓ to take ａ b ｉ n ｏｍ ial dis ｔ r ｉbution, t ｈ en incr ｅ as ｅ the nu ｍ b ｅ r of samples n、(提出一个有趣得问题就就是在统计分配，这就就是表明,标准正态分布就就是有效得 - 即从负无穷到正无穷得积分等同于一个,并在这样做表明推导了部分正常得 PDF 。我,我得一个朋友决定尝试推导出正常得 PDF 与沿中心极限定理指出，任何概率分布得均值作为试验增加得正常思维。这个推导就就是众所周知得。 但我们问自己如何正态分...
