Instructor: Balazs Rath

My hand-written, scanned lecture notes:

July 2 (combinatorics: multiplication rule, race horses):

page 1, page 2, page 3.

In Tim's lecture notes : page 2-4.

 

July 3 (combinatorics: permutations, combinations, divisions, poker):

page 4, page 5, page 6, page 7, page 8, page 9, page 10.

In Tim's lecture notes : page 4-10.

 

July 4 (combinatorics: multinomial coeeficients, maximum likelihood estimate; axioms of probability: set arithmetic):

page 11, page 12, page 13, page 14, page 15, page 16, page 17. page 18, page 19, page 20.

In Tim's lecture notes : page 10-15.

 

July 8,9,10,11 (replacement instructors)

In Tim's lecture notes : page 15-34.

 

July 15 (gambler's ruin, job applicant choice problem, Simpson's paradox, Monty Hall problem):

page 21, page 22, page 23, page 24, page 25, page 26, page 27, page 28,

In Tim's lecture notes : page 34-38.

More info about Simpson's paradox: wiki

More info about the Monty Hall problem: wiki

If you want to read more about the talk show host Monty Hall: wiki

 

July 16 (random variables, indicator, Ber(p), Bin(n,p), Geo(p)):

page 29, page 30, page 31, page 32, page 33, page 34.

In Tim's lecture notes : page 39-40.

 

July 17 (discrete R.V.'s, total mass of mass function is 1, NBin(r,p), expected value of Geo(p)):

page 35, page 36, page 37, page 38, page 39, page 40, page 41, page 42, page 43, page 44, page 45.

In Tim's lecture notes : page 40-46.

 

July 18 (expected value of Bin(n,p), expected value facts, variance, Chebychev's inequality):

page 45, page 46, page 47, page 48, page 49, page 50, page 51, page 52, page 53, page 54.

In Tim's lecture notes : page 46-52.

 

July 22 (Variance of Geo(p), Poisson r.v.'s):

page 54, page 55, page 56, page 57, page 58, page 59, page 60, page 61, page 62.

In Tim's lecture notes : page 52-57.

To recall (differentiation of) power series, take a look at the April 2 lecture of my MATH105 lecture notes

To recall the Taylor series of e^x, take a look at the April 4 and April 7 lecture of my MATH105 lecture notes

 

July 24 (continuous r.v.'s, probability density function, cumulative distribution function, Unif[a,b], Exp(lambda)):

page 63, page 64, page 65, page 66, page 67, page 68, page 69, page 70, page 71, page 72.

In Tim's lecture notes : page 58-64.

To recall basics of integration, take a look at lectures from January 29 to February 7 of my MATH105 lecture notes

In particular, Fundamental Theorem of Calculus: February 3 and February 5 of my MATH105 lecture notes

 

July 25 (expected value, variance and memoryless property of Exp(lambda) distribution, normal distribution):

page 72, page 73, page 74, page 75, page 76, page 77, page 78, page 79, page 80.

In Tim's lecture notes : page 64-73.

 

July 29 (normal distribution examples, joint p.m.f., joint p.d.f., marginals):

exercise handout page 80, page 81, page 82, page 83, page 84, page 85, page 86, page 87.

In Tim's lecture notes : page 73-78.

To recall basics of double intergrals and polar coordinates, take a look a look at Chapter 17.1, 17.2, and 17.5 of this book

 

July 30 (continuous marginals, independence of random variables):

page 87, page 88, page 89, page 90, page 91.

In Tim's lecture notes : page 78-80.

 

July 31 (uniform distribution and areas, covariance, variance of sums of r.v.'s, correlation):

page 91, page 92, page 93, page 94, page 95, page 96, page 97, page 98, page 99.

In Tim's lecture notes : page 80-85.

 

August 1 (convolution, Gamma distribution, convolution of normals, conditional p.m.f. and p.d.f.):

page 99, page 100, page 101, page 102, page 103, page 104, page 105, page 106, page 107, page 108.

In Tim's lecture notes : page 86-93.

 

August 5 (conditional expectation, least squares estimate, law of large numbers, central limit theorem):

page 109, page 110, page 111, page 112, page 113, page 114, page 115, page 116, page 117, page 118.

In Tim's lecture notes : page 93-96 and 103-104 and 108.

About Avogadro's number

 

August 6 (central limit theorem for sums of uniform, exponential and Poisson variables):

page 119, page 120, page 121, page 122, page 123.

About Stirling's formula

About the convolution of three Unif[0,1] r.v.'s

 

August 7 (central limit theorem exercises: widgets, airplane overbooking, roulette loss, gravel creation):

page 124, page 125, page 126, page 127, page 128, page 129, page 130, page 131.

In Tim's lecture notes : page 109-110.

About the log-normal distribution

 

August 8 (C.L.T. or Poisson approximation?, C.L.T. example: republicans, Poisson merging and coloring, examples):

page 132, page 133, page 134, page 135, page 136, page 137, page 138, page 139, page 140, page 141.