assets An asset is a commodity that provides a flow of services over time. +E.g. a house, or a computer. .A financial asset provides a flow of money over time -a security

From Individual to Market Demand Functions Think of an economy containing n consumers, denoted by= 1, .. ,n. Consumer is' ordinary demand function for commodity j is

In this lab session, the cantilever and fixed-fixed beams will be mechanically tested to determ material and device performance characteristics. The structures will be mechanically loaded the corresponding deflection measured. From the load versus deflection curves, an effective

This is an open book, take-home quiz. You are not to consult with other class members or anyone else. You may discuss the solution to this exam only with the course staff

Electric Fields 918.1 Conductors in electric field 1. Conductors A conductor is a material in which the electrons at the outer periphery of an atom have no great affinity for any particular individual

Random walks 1 Random walks a drunkard stumbles out of a bar staggers one step to the right, with a canal lies y steps to his right. Thi I equal p second, he either staggers one step to the left or probability. His home lies r steps to his left, and everal natural questions, including 1. What is the probability that the drunkard arrives safely at home instead of falling into the canal? 2. What is the expected duration of his journey however it ends? The drunkard's meandering path is called a random walk. Random walks are an im- portant subject, because they can model such a wide array of phenomena. For example

1 Graphs and Trees The following two definitions of a tree are equivalent Definition 1: A tree is an acyclic graph of n vertices that has n-1 edges Definition 2: A tree is a connected graph such that Vu, v E V, there is a unique path connecting u to u. In general, when we want to show the equivalence of two definitions, we must show

1 Sums and approximations Problem 1. Evaluate the following sums Solution. The formula for the sum of an infinite geometric series with ratio 1 /2

Notes for Recitation 13 Basic Counting Notions bijection or bijective function is function:x→ such that every element of the codomain is related to exactly one element of the domain. Here is an example of a bijection:

1 Conditional Expectation and Total Expectation There are conditional expectations, just as there are conditional probabilities. If R is a random variable and e is an event, then the conditional expectation Ex(r e)is defined