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If $X\sim \Gamma(a,\sigma_x^2)$ and $Y\sim \Gamma(b,\sigma_y^2)$. What will be the probability density function of R? Where $R=\frac{X+C}{X+Y}$, here $C$ is a positive constant, $\Gamma(.,.)$ denotes standard gamma probability density function and '$\sim$' represents 'distributed as'. X and Y are independent random variables.

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    Yes its correct as title says "Ratio of correlated gamma...." because it is ratio of X+C to X+Y where$X$random variable is related to both numerator and denominator whether$X$and$Y$are independent r.v.2011-12-16

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Please see the answer in link text