Suppose $X_i$ are distributed exponentially with rate $\lambda_i,i=1,2.$ Calculate $\Pr(X_1
I tried to change it into $\int_{0}^{\infty}Pr(X_2>x|X_1=x)dx$, but I have no idea how to do the integration.
Suppose $X_i$ are distributed exponentially with rate $\lambda_i,i=1,2.$ Calculate $\Pr(X_1
I tried to change it into $\int_{0}^{\infty}Pr(X_2>x|X_1=x)dx$, but I have no idea how to do the integration.
It will be convenient to call $X_1$ by the name $X$, and $X_2$ by the name $Y$.
To compute the probability, we must make certain assumptions. You are probably expected to assume that $X$ and $Y$ are independent. Then you can easily find the joint density $f(x,y)$ of $X$ and $Y$: it is the product of the individual densities.
Draw the line $y=x$. We want the probability of lying above that line. This is $\int_{x=0}^\infty \left(\int_{y=x}^\infty f(x,y)dy \right)\,dx.$
In this case, you can probably immediately write down the inner integral.