Estimate exponential distribution parameter

[Gauss M.D.]

Homework Statement

A certain type of transistor has an exponentially distributed time of operation. After testing 400 transistors, it is observed that after one time unit, only 109 transistors are working.

Estimate the expected time of operation.

Homework Equations

The Attempt at a Solution

It was suggested that I approximate with

X ≈ Bin(400,p)

Then conclude that p can be estimated with p* = 109/401 = e^-1/μ

That part I don't get is: why is p = e^-1/μ ?

 

[mfb]

In an exponential distribution, what is the probability that something survives for a time t? Then set t=1.