Let X denote an exponential random variable with unknown parameter λ >0 . Let Y = ζ (X > 5), the indicator that X is larger than 5. Recall the definition of the indicator function here is:

ζ(X>5)= 1 if X>5
0 if X<=5

We think of Y as a censored version of the Exponential random variable X: we cannot directly observe X, but we are able to gather some information about it in this case, whether or not X is larger than 5.).

Observe that Y is a Bernoulli random variable. Thus, the statistical model for Y can be written ({0,1}, {Ber (f (λ))} λ>0)for some function of f of λ.

What is f (λ)?