Math Fun

Saw a post at which piqued my interest. Before you read it, first think about the odds of a mother having 3 children on the same day of the year. How likely (or unlikely, as the case may be) would you guess it is? Turns out it's a lot more likely than most people would think. OK, now you can click the link.

FWIW, thanks to my recently revived statistical knowledge, I did pick up that the correct odds wouldn't be 365*365*365, but rather just 365*365. That's because once the first kid is born, the chance of him being born on that day is exactly 1 (unless she's a Chinese gymnast in which case she'd be born 3 years later). Think of that the next time someone asks, "what are the chances of that happening again?". The answer is, the same as the chances that it happened in the first place (assuming the factors haven't changed, of course).

I also realized that the odds of same day births would probably be lower due to the dates of conception being non-independent. For instance, my wife and I planned to have our kids in the spring because she didn't want to be pregnant during the heat of the summer. So the range of possible days our kids could have been born is only a window of about 100 days. Would you believe they were all born inside that window? (Actually, one of them did sneak in a bit late, but within a decent margin of error).


An Electric Lighting Audit

A while back I did an energy audit in my house. Fortunately for me I do live in an area served by cheap hydroelectric and coal energy. Well, fortunately for my pocketbook anyway. Regardless, I'm ever attempting to reduce my energy needs for both personal and altruistic reasons, hence the audit.

I surveyed all the lights in my home, noted their location, type, wattage, etc. When we moved in, most of the lights were old school incandescents. Altogether they added to 2918 watts of lighting. By swapping in a few compact fluorescents I've reduced that total to 1778. That's a savings of 40%. Impressive, but not so fast. Are all those lights used the same amount? Definitely not. The garage lights are on for probably only 10 minutes per day, on average. So clearly we need to factor actual usage into the equation.

So I also estimated the average usage of each bulb. Yes it was as fun as you think. What I found is that our 2918 watts account for about 4950 watt hours of actual usage per day. After my upgrades that dropped to 3274 watt hours, for a savings of 34%. If you notice that's less than the 40% we calculated earlier you get a brownie point. Indeed some of the lights we use the most are ones that I cannot reduce any further.

Even more interesting is something I've recently come to understand as I make a concerted, although to many unquestionably bizarre, attempt at understanding statistics. Quite often a very small number of things will often account for most of your results. A good example is the US federal budget. While McCain notably complained about earmarks in bills (which may be undesirable for many reasons) they account for a very small fraction of the money spent. If you want to make any reasonable dent in the outlays your best bet is defense, social security and medicare/medicaid which account by themselves for 65% of our expenditures.

Getting back to the original point (and hopefully avoiding a political tangent), I found that just a few of the lights in the house account for the majority of the electrical usage. In fact, the two sets of fluorescent lights in the family room account for nearly 60% of the total electricity. Even if I were to upgrade the rest my bulbs to compact fluorescents, it would only decrease my current usage by another 15%. I'm pretty much bound by those two sets of lights.

The exercise was a useful one. I'm on a slow quest to analyze all the electrical usage in the house. The light bulbs were the easiest to tackle. Some time I'll move on to the appliances and computers. The latter I'm rather apprehensive about. I might rather be ignorant.

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