04/26/06

12.4.2 Reading
1. Difficult - I do not understand why E9aX+b)=a(EX) +b and var(aX+b)=a^2var(X). Dot ey mean by linear transformation shifting the lines on a graph around? Also is the joint probability distribution the same as saying the probability of the two events... like does P(X=1, Y=1) = P(male with gout... XandY).
2. Reflective - I think I see now why you said this was the same thing as before but just organized. I think I seem to understand this better, surpisingly, even with all the funny notation better than perviously. (ex... independence is defined as P(XbelongingtoA, Y belongingtoB) = P(XbelongingtoA) x P(Ybelonging to Y) is the same as P(X=x, Y=y) = P(X=x)P(Y=y) is the same as P(XandY) = P(X)P(Y) which is what we learned before.

04/21/06

12.4.1 Reading
1. Difficult -
So if I am reading this correctly, the whole X thing is just assigning outcomes numbers?
2. Reflective -
I am reminded of how in High School we graphed those step-like graphs (I forget the name)... and there was a sort of equation for each line or something... but I don't see how the two connect...

04/19/06

12.3.4 Reading
1. Difficult -
I am unclear as to how 12.15, 12.16 and 12.17 come together to form the Bayes Formula. Is it just plugging and rearranging?
2. Reflective -
The hemophilia/pedigree example is especially helpful because on my Bio AP test there was a difficult question on probability in a pedigree. This should be helpful in the future.

04/17/06

12.3.3 Independence
1. Difficult -
Now that the book has defined independence I am confused as to what is conditional and what is independent. I understand why the coin toss in independent, but it seems like the coin toss is kind of like the child example. I am wondering why having two children is conditional while tossing a coin twice is independent. It seems like having children is equally random too (it can be a boy or a girl each time)... I don't understand what is independent and what is conditional. I also do not undertand the pairwise independent property.
2. Reflective -
I wonder why the phrases "pairwise disjoint" and "pairwise independent" share the word "pairwise."

12.3.2 Reading

1. Difficult -
I find the law of total probability, the equation difficult to "attach" with the problem. I see intuitively how that works (the whole multiplying the two probabilities and then adding them up), but I'm not really getting the P(A) = the sum of P(AB_i) P(B_i) as i=1 goes to n.
2. Reflective -
So, if I am understanding the tree diagrams correctly... as you said the lines connecting outcomes/events are like "ands" and should be multiplied (e.g. 1/200 times 0.99) ... and because we are interested in a positive test result we need to ADD opposite branches... (that is add the 199/200 times 0.5)... as they are not connected by a branch. So not only do "Ors" work with separate trees as the examples you gave us but on the same tree, just different paths? The paths need to be added up right? It sort of makes sense and the paths are not directly connected with a "branch."

12.3.1 Reading

1. Difficult -
I do not understand the Conditional Probability as it pertains to the Venn Diagram. I understand it through the explanations and through the calculations but not through the Venn Diagrams. This might be because I still don't thoroughly understand De Morgan's Laws.
2. Reflective -
What was explained in this section seems intuitive... it makes sense to minus one 'choice' from the numerator of example 2, as and just multiply them. It's kinda like the problems where we used 5! or something... The first place had 5 possible choices, the second 4 as one was gone, and so on and so forth.

12.2.2 Reading (w/o The Mark Recapture Method)

1. Difficult -
I didn't find this section that difficult, but I do have a "what if" question about the "Application from Genetics". I was wondering if there was a way to find the probabilities without doing the chart and getting every single outcome? (As in, could we assume what the possible outcomes are just by looking at cC and cC... that could make CC, Cc, or cc. Could we find the probability of each without knowing that there are exactly 2 possible offspring that could have Cc, and one each for CC and cc? Could we find them if we know the all types of possible outcomes but not how many of each for example if we had a ridiculous number of allele types?)
2. Reflective -
I thought this section was very interesting because the way it went about explaining probabilities as k/n and as a series of steps was WAY more understandable than my old trigonometry book back in high school (which strangely enough might have been made by the same manufacterer as this book... it too had a lot of blue in the pages as well as a timeline of Mathematician's lives in the front cover...).

12.2.1 Reading

1. Difficult -
I don't understand the differences between De Morgan's laws... the shaded Venn Diagrams. I also do not understand what the "pairwise disjoint" is. I don't understand how A_i U A_j = 0 when i does not equal j...
2. Reflect -
I think I understand how we are going to use the property P(A^c) = 1 - P(A). If I remember correctly we will be using that for problems that ask something like "What is the probability that you will not choose a red ball?" (You'd have the information to find the probability of getting a red ball and then subtract that number from 1 to get the probability of not choosing a red ball.

12.1.1 - 12.1.4 Reading

1. Difficult - I am blanking on the explanation the book gives on permutations. I understand logically why we remove one 'outcome' for each 'place' when we calculate but the blue box I do not understand as well as the simplification to
P(n,k) = n! / (n-k)!
I don't understand where the n(n-1)(n-2) x (n-k+1) is coming from.

2. Reflective - Haha, this section is giving me bad flashbacks of high school trig when I didn't understand any of the problems that use/d a combination of counting techniques. We also did very similar problems that dealt with the same items: cards, license plates, colored balls in a bag, etc.
I think I need to get this under my belt because it seems to be simple for everyone else and because if I decide not to do medicine and pursue ecology or something I will need to know these probability/statistics techniques very well in order to do research (i.e. maybe something like how many different types of fly can exist with the following traits: regular wings v. vestigial wings, red eyes v. white eyes, etc. We did something similar in Biology AP with Drosophilia).

HW0

(a) Tina Marcroft
(b) Math courses taken here: Math 3B
(c) I like the satisfaction I get after completing what I think might be a difficult problem. I'm not sure what area I'm especially strong in or weak for that matter. I think my performance is pretty much the same throughout all the different types of math I've done.
(d) The only time I can really remember not getting something was actually when I learned some probability in my high school Trigonometry class that I took 3+ years ago. After counting and simple combinations, which were pretty easy, I could not really figure out the more complex problems...(The answers ended up something like 5! times 4C5 over 4! for example... something that didn't follow the equations we derived.) It could have just been I took it too early because it seems like some things that I didn't understand in the past, I can easily understand now. I think the other thing I didn't get in that class was also her complex simplification exercises that you needed to solve with the trigonometric formulas like cos^2theta + sin^2theta = 1. They puzzled me exceedingly.
(e) Actually I liked that tough Trig teacher. She derived/proofed a lot of the formulas so the concepts were easier to understand.
(f) My worst math teacher taught my Stats class in high school. She just gave us the formulas, explained what each formula did in general (i.e. "you use ___ when you need to find ____") and all I had to do was plug and chug. I always finished my homework during the 10 minutes of class she allowed us to do so. I don't think I throughly understood the concepts as there was a stats question on my biology ap final in high school that delved somewhat into the concepts. I had no idea what that question was asking even though we had done those chi stats problems in class.
(g) 2E
(h) Finals are kept for a quarter. After that students can pick them up if they want. If they are not picked up by the end of the second quarter after the final was given, they will be recycled.
(i) A semi-late assignment is homework turned in during class and not before as it should; that is, the semi-late assignments are turned in between 9:10 and 9:50. They get a maximum of 10 points for completeness. Individual problems will be graded in passing.
(j) The 5 minute rule is that whenever I see/stop you, anytime, you must talk to me for at least 5 minutes.