Hello ! I am struggling a bit with this probability exercise. Thank you very much for any help with the problem !

X is a continuous random variable distributed following an exponential law of parameter z with a density

Fx(x) = z*exp(-z*x) when x>= 0

Fx(x) = 0 when x<0

1)Write the expression of the distribution function of X and give the probability that X goes above the value x= 1 when z = 1

I found it by searching on wikipedia, however I don't know how to find it from the density. Was I supposed to derive this expression ?

F(x) = P(X <= 1)

F(x) = 1 - exp(-1*1) = 1 - exp(-1)

So for X’s value to go above 1 : 1 – (1 - exp(-1))

2)Using the maximum likelihood method, give the expression of the estimator of z

I do not know at all how to proceed for this question