Subject: How is the half life of radioactive elements measured if it's very large?

I see a couple other people have asked this, but I am still wondering about 
elements with very large half lives (e.g. U238 - 4 Billion years, I think?)

I understand that a large sample will have enough atoms decaying that they can 
be measured.  Also we can determine the amount of the element present in a 
sample.  But if decay is a completely random process (and random is the key to 
my problem), and the half life so long, how can we be sure of the results?  

Are uranium samples monitored for years?  Even that wouldn't seem to yield a 
significant sample size, statistically speaking.  What kind of confidence 
interval can be attained with such a small sample?  Maybe I'm missing some 
fundamental understanding of the process.  I just can't wrap my mind around 
determining a number so large (!) from a process of random decay measured over 
a "short" period of time.  Any clarification you can offer is greatly 
appreciated!

Re: How is the half life of radioactive elements measured if it's very large?