Exponential distribution with an unknown parameter, theta

I don't actually know what topic this falls under exactly to be honest. The question goes:

*In an experiment to study pulses along a nerve fibre, the times between 101 successive pulses were measured. The $\displaystyle n=100$ observations gave a sample mean $\displaystyle \bar{x}=26.05$ seconds. Assuming that these data are a random sample from an exponential $\displaystyle Exp(\theta)$ distribution, calculate*

**(i)** the most likely value for the mean pulse rate $\displaystyle \theta$ per second

**(ii)** the most likely value for the probability $\displaystyle \phi$ that the time between successive pulses is greater than 20 seconds i.e. $\displaystyle \phi=P(X>20)=e^{-20\theta}$.