1 - Assume X + Y are independent standard exponentially distributed random variable. Derive the density of X + Y

2 - If X is exponentially distributed with mean 1, what is the distribution of e^-x

3 - In some random experiment Tn is a consistent estimator of Theta

Is log (Tn) a consistent estimator of log (Theta)?

Assume Xn is a sequence of random variable which converge in distribution to X

Is TnXn a consistent estimator of Theta X

I really appreciate any help.

Thanks,