PY 410, Statistical and Thermal Physics, Spring 2012

Homework 1 (Due Feb. 2^nd), problems from Reif: 1.1; 1.4 (analyze the answer at large N), 1.5, 1.9, 1.10, 1.12, 1.14

Additional Problem.* A person throws dice N times. Find the probability distribution of the maximum score for different N. Write down your results explicitly in a table for N=1,2,3 (use decimal numbers not fractions). Discuss the asymptotical form of this distribution when N is large. Solutions

Homework 2 (Due Feb 9^th), problems from Reif: 1.16, 1.17, 1.18, 1.23, 1.26*, 1.28* Solutions

M&M problem. This problem consists of three parts

1. Each of you will get a Pack of M&M mini. Each pack contains candies of six colors: Blue (Bl), Brown (Br), Green (G), Orange (O), Red (R) and Yellow (Y). You will need to count number of candies of each color and send the data to a designated person. The sample data you need to send should look like this
Bl – 27
Br – 23

            G – 18
            O – 25
            R – 31

Y – 34

Please send the data by Thu, Feb. 2^nd. Please do not invent the data; it is important that you do actual counting.

2. Now you can eat your candies, discard them, or share with your friends.

3. After all data is collected you will get back a table containing the results from the whole group. Each of you need to independently perform the statistical analysis of the data and answer the following questions.

· Estimate the variance and the mean for the number of candies of each color. Are these results consistent with the Poisson distribution?

· Estimate the variance of the sum of B-candies (i.e. blue + brown). Is it approximately equal to the sum of variances? Are the blue and brown colors statistically independent?

· Estimate the variance of the total number of candies (i.e. blue + brown + green + orange + red + yellow). Are all colors statistically independent? Explain your result.

· Plot the distribution function (in mathematica, excel, or any other software) for all colors (or all colors except red) from all students, i.e. the horizontal axis should be the number of candies and the vertical axis is the normalized frequency of occurrence of this number. The total number of data points should be 6 x number of analyzed packs. Fit this distribution to the Poisson distribution and Gaussian distribution. Which if the distributions work better? Argue why.

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	Q	Total
Blue	43	26	27	24	25	27	32	35	31	27	38	27	25	27	31	24	32	29	530	Blue
Brown	28	38	30	42	30	29	36	30	31	34	27	39	40	34	36	32	36	36	608	Brown
Green	22	30	33	27	35	25	30	28	33	26	30	20	30	33	31	27	34	29	523	Green
Orange	33	19	36	38	32	30	18	30	28	40	32	37	27	37	26	29	35	28	555	Orange
Red	43	46	41	39	41	54	47	34	35	41	45	36	47	41	34	45	42	47	758	Red
Yellow	33	39	33	31	36	36	31	42	39	32	27	41	33	23	40	28	21	30	595	Yellow
Total	202	198	200	201	199	201	194	199	197	200	199	200	202	195	198	185	200	199	3569	Total (all colors)

note: 12/18 packs have red as max.!

Lecture5

Lecture6

Homework 3 (due Feb. 16^th) problems from Reif: 2.1, 2.2, 2.4, 2.8, 2.10 Solutions

Lecture7

Lecture8

Homework 4 (due Feb. 23^rd) problems from Reif: 3.1, 3.3, 3.4; Problem 4* Solutions

Lecture9

Lecture10

Homework 5 (due Mar 1^st) problems from Reif: 2.11, 3.5, 3.6 Solutions

Lecture11

Lecture12

Homework 6 (Due March 22^nd) – problem 1 on page 5, problem 4 on page 6, and problem 3 on page 7 in the notes (lecture 11), Solutions Problems from Reif: 4.1, 4.2, 5.1, 5.2, 5.3, 5.4. Solutions