X~U(0,2π)
分布函数F(y)=P(y)=P(Y<=y)=P(cosx)<=y)=P(arccosy<=x<=2π-arccosy)
=(1/2π)(2π-arccosy--arccosy)=(1/2π)(2π-2arccosy)
=1-arccosy/π
概率密度函数f(y)=F(y)'=1/(π(1-y^2)^(1/2)) -1<=y<=1
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/2cf5e0fe9925bc313cac1ee54edf8db1ca1370dd?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
扩展资料
随机数据的概率密度函数:表示瞬时幅值落在某指定范围内的概率,因此是幅值的函数。它随所取范围的幅值而变化。
密度函数f(x) 具有下列性质:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/622762d0f703918f542622b7413d269758eec4dc?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)