Suppose that X1, X2 are i.i.d. exponential random variables with mean 1, i.e., their densities are given by e^-xfor x > 0. Compute

1. E[X1|X1 + X2].

2. P(X1 < 3|X1 + X2).

3. E[X1| min(X1, t)].

4. E[X1| max(X1, t)].