# Thread: Simple exponential function questions

1. ## Simple exponential function questions

Given $X_1,X_2,X_3$ are independent and exponentially distributed random variables with respective rates $\lambda_1,\lambda_2, \lambda_3$.

How can I derive $P(X_1=min(X_1,X_2,X_3))$.

In fact I know the answer, it should be $\frac{\lambda_1}{\lambda_1+\lambda_2 + \lambda_3}$.

Meanwhile I also know that $P(X_1

But I just can't seem to get it

3. What about $P(X_1 ?