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I have the following random variable ##X=\frac{a_1}{a_2+1}##, where ##a_i=b_i/c_i##, where ##b_i## and ##c_i## are exponential random variables with mean 1. I need to evaluate the CDF of ##X## as

[tex]F_X(x)=Pr\left[X\leq x\right]=Pr\left[\frac{a_1}{a_2+1}\leq x\right]=\int_0^{\infty}Pr\left[a_1\leq x(a_2+1)\right]f_{a_2}(a_2)\,da_2[/tex]

I found the CDF and PDF of ##a_i## as ##F_{a_i}(x)=1-\frac{1}{1+x}## and ##f_{a_i}(x)=\frac{1}{(1+x)^2}##. My fist question is: are the limits of the integral above correct?

Thanks

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# B How to evaluate this CDF?

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