→ NCUflywind:我算出來C=(ln2/π)^0.5 E(X)=0 Var(X)=1/2ln2 02/04 00:19
→ NCUflywind:今天跟補習班老師確認過答案了~π前面沒有2哦~~~ 02/05 00:33
※ 編輯: DIDIMIN 來自: 140.127.200.211 (02/05 11:50)
※ 引述《Nocp (衝浪..被浪沖 傻傻分不清)》之銘言：
: Show that the constant C can be selected so that
: f(x) = C*2^ -x^2 , -∞ < x < ∞ , satisfies the conditions
: of a normal p.d.f . Hint write 2 = e ^ln2
: 請問 這是不是超過商統了... 700題裡!都沒看見= =
Given f(x) is a normal distribution, we can use the property
∞
∫ f(x)dx = 1
-∞
to find the constant C.
∞
∫ C exp(-x^2 ㏑2)dx = 1 → C = (㏑2 / π)^0.5
-∞
So, if C = (㏑2 / π)^0.5, then f(x) satisfies the nornal distribution
with mean 0 and variance 1/2㏑2.
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