It's been a while since I looked into this theory in any depth, but the wikipedia article should be useful.
Suppose you have a probability space where the sample space X = {a,b}. Let your sigma-algebra be the collection {empty, {a}, {b}, {a,b}}, and let the probability measure be P(empty) =...
Deming regression may be a useful starting point. Roughly instead of minimizing the summed squared residuals in the y direction, you minimize the perpendicular distance from the points to your line, thus taking into account both x and y error (scaling the errors if the errors in the x and y...
Voltage is measured between two points. One point is touching your arm, but what is the other point?
Or they do make non-contact voltmeters that, if I understand correctly, treat the surface you're measuring as one plate in a capacitor and the meter probe as the other plate and measure the...
I don't understand your question.
Transitivity means that if R(a,b) is true and also if R(b,c) is true then R(a,c) is true. If R(a,b) is not true or if R(b,c) is not true, then it says nothing about R(a,c).
Your example stated "1≥2" implying that you mean that statement is true and that...
Your example
"1≥2
2≥3
and 1≥3"
is true if you change what ≥ means so that it means less than!
Say R(a,b) means that a≥b.
Then R(2,1) is true because 2≥1.
R(3,2) is true because 3≥2.
That means R(3,1) is true for two reasons:
A. R(3,1) is true from transitivity because R(2,1) and R(3,2)
B...
Transitivity means R(a,b) and R(b,c) implies R(a,c).
If R(a,b) means that a≥b and R(b,c) means b≥c then is it clear that a≥b≥c so a≥c and so R(a,c)?
If R(a,b) then a^2 = b^2. If R(b,c) then b^2 = c^2. Substitution implies that a^2 = c^2 so R(a,c). Hence transitivity.
Does that help or have I...
Hi shinkansenfan. jwatts is right that you should be using the separate forums for homework questions.
But since you're here: If you are asking for the probabilities of the events in your questions, think about all the possible ways that two of five ordered items can be defective.
Consider a...
I did a little reading. I can't find an english translation of Cantor's paper, but I found a paper on jstor (http://www.jstor.org/stable/2975129) that discusses it. Corollary 2 of his Theorem 2 from "On a Property of the Collection of All Real Algebraic Numbers" is "The real numbers cannot be...
Isn't it just the definition? In practice, when you count a bunch of things, the number of items is one of the natural numbers. It's a bit like asking why 2 has the shape it does--it's just the definition we all agree on so we can easily communicate.
Or said another way: there's nothing magical...
I wondered about that, but is that really true? Why would it be normally distributed?
I thought peripatein meant that the error will be uniformly distributed between 0 and the size of the smallest gradation in the ruler (or something like that), but I don't know if that is true.
I do notice that if W had an error of 0.5 cm, then the error in the surface area would be around 0.5 cm * L = (0.5 cm)(122 cm) = 61 cm ^2 which is certainly close to 70 cm^2.
Others will surely have more insightful input!
[Edit. Just to be clear, though my argument is basically just half of...
Thanks for your thoughts! I'm not sure that I've failed to define the problem, though perhaps I didn't do it clearly here, but you are probably right that it would be better to directly model the corruption, so that the residuals would be much closer to independent. A problem is there is no...
Oh, there are 26 transitions in that sequence, yes. and 8 transition probabilities you need to calculate.
You should not divide the counts by 26, though. p(0|a,b) and p(1|a,b) should be divided by the number of times ab appears in the sequence.
001 011 100 101 011 110 000 101 001 1
0 010 111...
Oh, ok. As I have always seen it, a pipe | is used instead of a slash /. I will write p(b,c|a,b) to be the probability of transitioning from state (a,b) to (b,c).
I'm not sure why you say there are 26 possibilities, so I might be misunderstanding, but if I understand correctly:
To find the...