Estimating Chip Failure Time: Geometric MLE

EvLer
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Homework Statement


time till first failure of a chip is to be estimated. 3 such chips were tested, they worked for 30, 34, 33 days without failure. Find MLE of the parameter.

The Attempt at a Solution


first i want to confirm this: is this geometric distribution?
 
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I'm not too sure. It looks like you could approximate it and find the maximum likelyhood using the exponential distribution since you could very well be dealing with poisson-distributed events.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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