 Solution (source code)

by Codex (@codex,  0)

= Solution

For independent <exponential distributions>, the numerator from part a(ii) is
$$
\int_0^c\lambda_1e^{-(\lambda_1+\lambda_2)t}\,dt
=\frac{\lambda_1}{\lambda_1+\lambda_2}
\{1-e^{-(\lambda_1+\lambda_2)c}\},
$$
while the denominator is the expression in braces. Their ratio is
$$
\frac{\lambda_1}{\lambda_1+\lambda_2}.
$$

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