Yes, some of us do know the difference between stochastic and deterministic statistical analysis too, and can even do time series analysis with our eyes closed, however, your sample is somewhat flawed! You're talking about obsolete designs built in a whole different era. Chernobyl (a 1 GW RMBK design, which was known to be flawed from the design point to begin with) is so out of the league of modern reactors from a design and operations perspective, that there is not even a valid comparison. Unlike Chernobyl, modern reactors do not allow anyone to shut down their safety systems, as Chernobyl did, which is what caused the explosion in the first place as poorly trained operators tried to bring the reactor offline. Same with Three Mile Island, though newer, still obsolete. Not to mention the fact that reactor operations are governed today in a completely different manner than 30 - 40 years ago. But this, like anything else, is subject to human error, since humans build and run the systems. That's just a fact of life that isn't going to change, just like the politics involved in this or any other industry.
The French have enjoyed a stellar safety record, their politics aside....it works. Their worst nuclear "accident"? Three people walked into a nuclear particle accelerator in 1992 without wearing protective clothing, and were contaminated. I guess you really can't fix stupid??
Florida Power and Progress Energy are currently starting production of two plants here in Florida. It's about damned time. Hopefully we'll see more along the way.
Delaying the construction of power plants only serves to have the running life of existing units lengthened. Yeah, a nuclear reactor can run for 30 or 40 years without much trouble, if the vessel walls hold up as they were engineered. But I would rather see the timely replacement of such units then asking the existing equipment to do a job it really wasn't intended to do. There are reactors running today that should have retired, just based on their age, simply because they do not have replacement capacity for these units. Yeah, engineers can certify their suitability for operation, but why take that chance?
Spent fuel rods are stored onsite in pools, in a vault, and a working reactor needs a fuel change every 6 - 9 months or so, depending on its output and capacity. This does not make for lots and lots of waste such as people may think, though yes, there is spent nuclear waste. I was in the energy industry for 10 years here in the U.S., and I'll still take nuclear as a safe, clean, renewable fuel source over any other source of energy out there, all "analyses" aside. Ever see the crap that comes from coal combustion? Or from "cleaning" coal to make it suitable for combustion? It ain't pretty!!