Notes for Recitation 15 Problem 1. Learning to count takes practice! (a)In how many different ways can Blockbuster arrange 64 copies of 13 conversations about one thing, 96 copies of L'Auberge Espagnole and 1 copy of Matrix Revolutions on a shelf? What if they are to be arranged in 5 shelves?

Conditional Probability Suppose that we pick a random person in the world. Everyone has an equal chance of being selected. Let A be the event that the person is an MIT student, and let B be the event that the person lives in Cambridge. What are the probabilities of these events? Intuitively

It's really sort of amazing that people manage to communicate in the English language Here are some typical sentences: 1. You may have cake or you may have ice cream 2. If pigs can fly, then you can understand the Chernoff bound 3. If you can solve any problem we come up with then you get an a for the course. 4. Every American has a dream What precisely do these sentences mean? Can you have both cake and ice cream or must you choose just one desert? If the second sentence is true, then is the Chernoff bound incomprehensible? If you can solve some problems we come up with but not all, then do you get an a for the course? And can you still get an a even if you cant solve any of the problems? Does the last sentence imply that all Americans have the same dream or might

Diffusion: Read Plummer Chap. 7, sections 7.1-7.4,, 7.53, 7.5.8 Show that c(zt) Wroexpfzla)I,with a=2VDf, is a solution to Fick's second law of diffusion. ac(z, t) dc(zt) 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections)for As impurities in Si at 1100 C for two cases: 1)CAs=10 cm and ii)

Microelectronics Processing Technology Spring Term, 200. Quiz 1 90 min/90 points total March 19 2003 Note: Be brief and relevant in your answers, and use sketches. Show your work. k=1.3810-23J/K=8.6210-eV/K 40 1. Film deposition, CVD )Discuss briefly what factors affect the microstructure a film grown on a substrate

What does Materials Science have to do with Microelectronic Processing? Need to understand DIfferences: metals, oxides and semiconductors Atomic bonding Oxidation rates, compound formation(GaAs)

What Are We Doing in this Chapter? We expand our basic consumer choice framework to include the possibility that consumers can sell something to generate income. Again, in terms of theoretical framework, nothing is new

What Do We Do in This Chapter? We conduct comparative statics analysis of ordinary demand functions the study of how ordinary demands*(p,,P2,y) and x2*(p1,p2,y) change as prices1,P2 and income y change. Theoretically, nothing new

What Do We Do in This Chapter? We create a mathematical measure of preference in order to advance our analysis

What Are We doing in this Chapter? We apply our basic framework of consumer choice to study issues of choices across different time periods, e Again in terms of theoretical framework, not much is new!