$X_n$ is an i.i.d. random process with marginal exponential distribution: $$f_X(x)=\lambda e^{-\lambda x} \text{ when } x \ge 0$$ where $\lambda > 0$.
I am trying to find $P[X[n]-2X[n-1] < 0]$.
Even though $X_n$ is a random process, can I treat this problem as if I am trying to find the difference between two i.i.d. exponential distributions? Like:
$$A, B \text{~} Exp(\lambda) \rightarrow \text{Find } P[A-2B < 0]$$
If so, I can figure out the rest.