设随机变量X的密度函数为f(x)=Acosx,-π/2_数学解答

设随机变量X的密度函数为f(x)=Acosx,-π/2

人气：235 ℃　时间：2019-10-29 19:46:55

解答

F(x)=∫Acosxdx|[-π/2,π/2]=1
∫Acosxdx
=A∫cosxdx
=Asinx+C
F(x)=∫Acosxdx|[-π/2,π/2]
=sin(π/2)-sin(-π/2)
=A-(-A)
=2A=1
∴A=1/2
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