05/31/06

12.6.2 Reading

1. Difficult - So, is the CLT saying basically that as the sample gets larger, the better the approximation to F(x). Isn't this the same as the "Weak Law of Large Numbers"? Or wait, it says that F(x) is the dist. func. of SND so, how is it saying that it is approaching SND? How do we know that (I know it says it is not proven here)? Couldn't there theoretically be a skewed graph which would have the same mean and variance as a graph as a normally distributed graph? Isn't a skewed graph not SND?

2. Reflective - The approximating "function" of the CLT reminds me of... was is Poisson?... one of the distributions we learned about was approximating... I think it also depended on a very large n.

0526/06

1. Difficult - I don't understand what the difference is between "arithmetic average" and the expectation. They are essentially the same thing, are they not?
2. Reflective - 12.6.1 is pretty intuitive. It makes sense that the larger the sample the more reliable the expectation as it is "harder" for big samples to be wrong (there are more individual factors that need to be wrong... it is less likely that 10 pieces of data are all off than, 5 for example).

05/24/06

1. Difficult - I don't understand the book's explanation of "hazard rate"? Perhaps you could give us a graphical example?
2. Reflective - Too bad our lives cannot be predicted with a function... too many variables/environmental factors I think... (I'm looking at the aging example)... otherwise we could be better able to schedule waht we should and shouldn't do before we die.

05/22/06

1. Difficult - For example 18 why is the notation P(F(X) is less than or equal to u) instead of P(X=x)... is it not a density? Or does it signify you can use many functions for these problems?
2. Reflective - Why is the exponential distribution a "poor lifetime model"? Is it because in nature distributions are more erratic?

05/17/06

12.5.3
1. Difficult - Is there an intuitive explanation for the 12 for the variance formula (b-a)^2/12... the squaring makes sense but the 12 doesn't really (the calculations do make sense though).
2. Reflective - Are there special strange distributions like the Uniform Distribution (like for example one that forms a triangle? or a arc?)?

05/15/06

12.5.2
1. Difficult -
I thought we can't use integration for finding the area underneath the curve (ex. 8 and so on).
2. Reflective -
Are most stats/prob problems usually normally distributed?

05/12/06

12.5.2 The Normal Distribution
1. Difficult - How do we know in a problem if the sample is normally distributed? Must it say so explicitly or is there some way to figure that out?
2. Reflective - I was wondering last time if this was the same thing we did in Stat's class and it most definately is... I remember the beginning of stats class (after doing a bit of probability) we did do the whole "z" thing and looking up values on charts.

05/10/06

12.5.1 Reading - Continuous Distributions
1. Difficult - So do the points on the curve depend on what part of each histogram bar you choose to assign the point to? (Like in calc we chose to use the left hand, right hand corners or the middle to make the curve...)
2. Reflective - When it talked about the probability being the area under the curve that reminded me of statistics and the bellcurve. I seem to remember my teacher mentioning the area under the curve equaled 1... These continuous distributions must be where stats come from.

05/08/06

12.4.6 Continued
1. Difficult - So I'm wondering if I got this right... it seems all the Poisson problems deal with probabilities of expecting something... like "What is the probability that ____ will happen 2 times?" or "What's the probability that we'll find one ____?"
2. Reflective - I think by looking at these problems I can kinda see how the infinity fits in... like the questions don't ask "What's the probability that ___ will happen 5 times if I do _____ 20 times?" There doesn't seem to be a set number of events... perhaps because these are such rare events we don't need to.

05/05/06

12.4.6 The Poisson Distribution
1. Difficult - Wait, I totally forgot what the Poisson thing was in the first place... was it sort of like that binomial pyramid that was like:
1
1 1
1 2 1
1 3 3 1
Etc? And how did we use them? (I know it says proteins and stuff... but HOW would we use them? It says models, but models for what? For proliferaction... for shape or something?)

2. Reflective -
I remember doing "Poisson" problems in High school... I think trig class... but I don't remember what it was.

05/05/06

12.4.6 The Poisson Distribution
1. Difficult - Wait, I totally forgot what the Poisson thing was in the first place... was it sort of like that binomial pyramid that was like:
1
1 1
1 2 1
1 3 3 1
Etc? And how did we use them? (I know it says proteins and stuff... but HOW would we use them? It says models, but models for what? For proliferaction... for shape or something?)

2. Reflective -
I remember doing "Poisson" problems in High school... I think trig class... but I don't remember what it was.

05/03/06

1. Difficult - I don't understand how the g. distr. is the same as the series... I see the similarities... but the distribution is based on probability right?
2. Reflective - I do recognize the sums/series from Algebra 2/Trig (I forget which)... but it had simpler notation... I wish all my teachers (from elementary school and up) used the same kind of this kind of correct mathematical notation and shorthand... much confusion would be avoided. Oh well. (Really I wish all scientific/mathematical textbooks used the same standardized notation.)