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Posted: 02:03:48 PM, 21/05/2013

[Continued from Grasping the normal distribution (Part 4)]
Working the statistics
For my last trick, I'd like to show you how to use Equation 37 to compute statistical parameters like mean, variance, and standard deviation. For each of these parameters, we'll be evaluating integra......

Posted: 02:54:04 PM, 16/05/2013

[Continued from Grasping the normal distribution (Part 3)]
<b>What if I <i>want</i> areas?</b>
As we've discussed, the sum of the probabilities for all possible results must add up to unity. And indeed they do, in <b>Figure 8</b>. If, for a given &q......

Posted: 06:32:19 PM, 14/05/2013

[Continued from Grasping the normal distribution (Part 2)]
Computing the odds
It's time for a little math. Let N be the number of dice for a given experiment. The smallest value we can get from the throw comes when all the die are showing 1's, so the score must be N. Likewise, the......

Posted: 07:16:50 PM, 08/05/2013

Call it Hell, Call it Heaven, it's a probable twelve to seven
that the guy's only doing it for some doll—
Stubby Kaye and Johnny Silver, Guys and Dolls, 1955
In this column, we will tackle parameter estimation. This discipline is based on the fact that our knowledge of the state of......

Posted: 06:38:46 PM, 10/05/2013

[Continued from Grasping the normal distribution (Part 1)]
What are the odds?
A good definition for the word "probability" is hard to find. The ones I've found use synonyms like likelihood or chance, so the definition is circular. Fortunately, most of us have an innate understandin......

Posted: 10:32:16 AM, 21/06/2011

There's some exciting news about a product I've lived with—and sometimes praised, sometimes cursed—for decades: Mathcad, PTC's premier math analysis tool.
Regular readers know that most of my columns are math-oriented, as is most of my work. For that reason, I'm a hea......

Posted: 11:32:01 AM, 14/06/2011

Physicists know that many problems can be treated as though the dynamical event happened instantaneously. Examples might include the impact of a hammer and nail, two billiard balls colliding, or a baseball bat hitting the ball. Deep down, we know that there is a complex interaction involve. Materi......

Posted: 02:45:56 PM, 03/06/2011

Read the previous part here.
This is not an unreasonable approach, as long as you don't mind the 90 W part. A vertical descent is what we used for Surveyor and other unmanned missions. It simplifies the automated landing quite a bit, and you can change that landing longitude by making......

Posted: 06:38:09 PM, 02/06/2011

Click here to view the previous part.
This approach is, in fact, the same one adopted by Euler, Lagrange, and company. In their formulation of the RTBP, they wrote the equations of motion in the rotating system, which meant that they had to add centrifugal and Coriolis terms to the equati......

Posted: 01:10:15 PM, 31/05/2011

Read the first part here.
The three-body problem
One look at figure 1, though, tells you that this ain't your grandfathers ellipse. It's a strange and complicated trajectory, bending left, then right, then around the moon, in a sinuous path perhaps more familiar to a figure skate......

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