设随机变量X,Y独立,且均服从参数为λ的指数分布,求:X/(X+Y)的分布先算出Z=X+Y再算X/(Z)?f(z)=(λ^2)*z*e^(-λz)但Z与X不相互独立了,还要算f(z,x),很麻烦的样子有没有简单的算法?
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![设随机变量X,Y独立,且均服从参数为λ的指数分布,求:X/(X+Y)的分布先算出Z=X+Y再算X/(Z)?f(z)=(λ^2)*z*e^(-λz)但Z与X不相互独立了,还要算f(z,x),很麻烦的样子有没有简单的算法?](/uploads/image/z/4945816-64-6.jpg?t=%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX%2CY%E7%8B%AC%E7%AB%8B%2C%E4%B8%94%E5%9D%87%E6%9C%8D%E4%BB%8E%E5%8F%82%E6%95%B0%E4%B8%BA%CE%BB%E7%9A%84%E6%8C%87%E6%95%B0%E5%88%86%E5%B8%83%2C%E6%B1%82%3AX%2F%28X%2BY%29%E7%9A%84%E5%88%86%E5%B8%83%E5%85%88%E7%AE%97%E5%87%BAZ%3DX%2BY%E5%86%8D%E7%AE%97X%2F%EF%BC%88Z%EF%BC%89%EF%BC%9Ff%28z%29%3D%28%CE%BB%5E2%29%2Az%2Ae%5E%28-%CE%BBz%29%E4%BD%86Z%E4%B8%8EX%E4%B8%8D%E7%9B%B8%E4%BA%92%E7%8B%AC%E7%AB%8B%E4%BA%86%EF%BC%8C%E8%BF%98%E8%A6%81%E7%AE%97f%28z%2Cx%29%2C%E5%BE%88%E9%BA%BB%E7%83%A6%E7%9A%84%E6%A0%B7%E5%AD%90%E6%9C%89%E6%B2%A1%E6%9C%89%E7%AE%80%E5%8D%95%E7%9A%84%E7%AE%97%E6%B3%95%EF%BC%9F)
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