# Let $x_1=\exp(\lambda_1),x_2=\exp(\lambda_2)$, $x_1, x_2$ are independent show $P(x_1<x_2)=\frac{\lambda_1}{\lambda_1+\lambda_2}$ [closed]

Let $$x_1=\exp(\lambda_1),x_2=\exp(\lambda_2)$$, and $$x_1, x_2$$ are independent random variables.

Show that $$P(x_1

## closed as off-topic by Lord Shark the Unknown, Wouter, Thomas Shelby, MickG, StrantsMar 19 at 19:45

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$$P(X_1
$$=\lambda_1\cdot \lambda_2\cdot\int_0^{\infty} e^{-\lambda_2\cdot x_2}\cdot \left( \int_0^{x_2} e^{-\lambda_1\cdot x_1} dx_1 \right) dx_2$$