Lecture 1
Make sure that you define what a and b represent when doing problems for homework and on exams.
Also, clearly
indicate the probabilities of a and b when you define them.
Box your final answers.
The formula (a+b)
n
can be used for all higher order problems.
We need a way to expand this general formula.
Rules for the expansion of a binomial:
1.
N, the exponent is the sample size.
The power "n" is the number of events.
If we have 2 coins, n = 2.
If we have 3 coins,
n = 3.
If we have a family of 3, n = 3, etc.
If you were asked the probability of 4 girls in a family of 9, n = 9.
The tossing
of the coin is the event.
The birth of the child is the event.
2.
The expansion of the binomial is to n + 1 terms: if n = 2, we will have 3 terms, if n = 3, we will have 4 terms.
3.
The first term is always a to the power of n (a to the n, b to the zero power).
4.
The last term is always b to the power of n (b to the n, a to the zero power).
5.
The a terms decreases by 1: a to the third, a to the second, a to the first power, etc.
6.
The b terms increases by 1: b to the zero, b to the first, b to the second power, etc.
7.
The first and last coefficients are always 1.
The inside coefficient is (the previous a exponent x the previous a coefficient)
divided by the previous rank.
Rank is the position of the term.
Always start on the left and work your way to the right.
You may use Pascal's Triangle, but mistakes due to memorization errors will lose points.
You get no credit unless you do
the problem correctly.
A math error will lose fewer points than getting the right answer the wrong way.
No calculators
will be allowed during the tests.
IN CLASS PROBLEM SET #3
Make sure you can do these on your own.
Don't sit back and let someone else do all the work in class.
You need to work quickly
because you will have a time constraint on the exam.
Do the problems in the back of the chapter  the answers are in the solution
manual.
On the exam, you will not have to take the math all the way through since no calculators will be permitted. It will also
help if you come prepared for class.
Another aspect of chance in genetics systems that we must consider is how to compare your results with the expected
. We
can compare predicted ratios with expected results.
We examined Mendel's actual data and ratios given in the first lecture.
We
had 2.84:1 and 3.01:1 and no one objected to rounding off to 3:1.
Another question we can ask of statistics is "how do we know
when a result we get matches the model?"
How do you determine whether data obtained in an experiment fits the model?
Even
the 3:1 ratio that Mendel got from his experiments was not exactly 3:1, but no one questioned his results.
Where do we draw the
line?
We can go back to the cointossing example.
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 Spring '08
 PRATT
 Cell Cycle

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