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MATH-111 (DUPRE) SPRING 2010 LECTURES
51. LECTURE FRIDAY 28 AUGUST 2009
We have previously discussed four basic rules for guessing and dened the notation E (X |K )
for our guess of the value of the unknown X based on the information in the statement K.
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1
1
1
E (Xn ) = E ( Tn ) = E (Tn ) = nX = X .
n
n
n
That is we nally arrive at a fairly remarkable result:
E ( Xn ) = X .
That means that whenever we take a sample, in advance of actually taking the measurements
w
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MATH-111 (DUPRE) SPRING 2010 LECTURES
the count for one second is simply an indicator of whether a single bus comes or not. Thus,
as n becomes very very large, the success count for a sample of size 1/n can be considered to
be an indicator of whether a
MATH-111 (DUPRE) SPRING 2010 LECTURES
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30. LECTURE FRIDAY 19 MARCH 2010
Today we had a review of condence intervals and the normal distribution.
31. LECTURE MONDAY 22 MARCH 2010
Today we discussed the t distribution and its use for calculating margins
MATH-111 (DUPRE) SPRING 2010 LECTURES
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49. LECTURE MONDAY 24 AUGUST 2009
We discussed the general rules for guessing unknown quantities so as to maintain logical
consistency. We use capital letters to denote unknown quantities and statements of unknown
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[n + 1]C [r + 1] = nCr + nC [r + 1].
To see why this is true, imagine a box containing n +1 blocks of which one is red and all the rest
are white. The outcomes for choosing r + 1 blocks can be separated into two s
MATH-111 (DUPRE) SPRING 2010 LECTURES
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We can apply this to the variance of a total, since V ar(X ) = Cov (X, X ). This is similar to the
special case for numbers of squaring a binomial
(a + b)2 = a2 + b2 + 2ab.
With covariance, it takes the form
V ar(
MATH-111 (DUPRE) SPRING 2010 LECTURES
5
1
.
3
On the other hand, suppose that for real number r, we let (r) denote the statement the
number up on the dice is the number r, so exactly one of the statements (1),(2),(3),(4),(5),(6)
is certainly true for the
MATH-111 (DUPRE) SPRING 2010 LECTURES
1. LECTURE MONDAY 11 JANUARY 2010
We discussed the syllabus and course policy as well as the location of my o ce and my o ce
hours. I will generally be in my o ce Monday, Wednesday, and Friday from 9 to 10 AM and
fro
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MATH-111 (DUPRE) SPRING 2010 LECTURES
E (X + Y |K ) = E (U + V |K ),
which is to say that our guess for the value of X + Y has to be the same as our guess for U + V.
Again, if we write E (X |K ) = a and E (Y |K ) = b, then by the retraction rule, we hav
MATH-111 (DUPRE) SPRING 2010 LECTURES
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In general with two unknowns we look for a simple linear relationship, and this means that
if we graph the value y we guess for Y when the value of X is given to be the number x, this
straight line must go right t
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E ( X | A) = v A ,
E (X |B ) = vB ,
E (X |C ) = vC ,
E (X |D ) = vD ,
E (X |F ) = vF .
Then our formula says
E ( X ) = v A P ( A) + v B P ( B ) + v C P ( C ) + v D P ( D ) + v F P ( F ) .
Thus, knowing the values