CS578/STAT590: Introduction to Machine Learning Fall 2014 Problem Set 1 Joon Hee Choi Handed In: 09/14/2014 Review Questions 1. 2. 3. • ∂f ∂x = 6x − y − 11‚ ∂f ∂y • ∂f ∂x = 6x − y − 11 = 0‚ = 2y − x ∂f ∂y = 2y − x = 0 ⇒ x = 2‚ y = 1 ⇒ (x‚ y) = (2‚ 1) • (a) n = 2 w1 x1 and x = . Then‚ w2 x2 wT x + b = w1 x1 + w2 x2 + b = 0 ⇒ −x1b + Let w = w1 x2 − wb =1 2 (b) n = 3 w1 x1 Let w = w2 and x = x2 . Then‚ w3 x3 T w x + b = w1 x1 + w2 x2 + w3 x3 + b = 0 ⇒ −x1b + −x2b
Premium Harshad number
PROBLEM SET 4 1) Consider the following utility functions‚ where W is wealth: (a) U (W ) = W 2 1 (b) U (W ) = W (c) U (W ) = −W (d) U (W ) = W (e) U (W ) = ln(W ) (f) U (W ) = W 1−γ ‚ with γ = 2 1−γ How likely are each of these functions to represent actual investor preferences? Why? 2) Suppose investors have preference described by the following utility function with A > 0: U = E(r) − 1 Aσ 2 2 Each investor has to choose between three portfolios with the following characteristics:
Premium Risk aversion Utility Investment
Problem Set 1 Complete all questions listed below. Clearly label your answers. 1. The receipts and year of release of the five movies with the largest nominal box office revenues‚ along with the CPI data of each year are presented below. Assuming that the receipts for each of the movies were derived during their year of release‚ convert the receipts for each to real dollars for the year 2010 (2010 CPI 230.1). Put the movies in order from largest to smallest real box office receipts and show
Premium Economics Inflation Unemployment
PROBLEM SET 4 Name: ______________________________________________ Problem Set 4 is to be completed by 11:59 p.m. (ET) on Friday of Module/Week 8. 1. Movies are distributed in a variety of forms‚ not just first run theatrical presentations. What other ways are movies distributed? What are the different price points? Using this information‚ draw a fully labeled graph of the market for movies in which the distributor of the film price discriminates. (NOTE: This should not be perfect price
Premium Game theory Marketing
ECN171 Economy of East Asia Problem Set 1 The data for this problem set is posted on SmartSite in the Resources folder. It was downloaded from the Penn World Tables version 7.1‚ which is publicly available at https://pwt.sas.upenn.edu/php_site/pwt_index.php . 1. Graph the GDP [per capita] of the East Asian countries in PS1_data.xls on one graph. Which East Asian country is the largest [richest] in 1960? In 2010? When did the switch occur? 2. Calculate the growth rates (log difference‚ using natural
Premium Asia East Asia South Korea
Problem Set 3 Name: Lauren Hensley Problem Set 3 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 6. 1. Data for the market for graham crackers is shown below. Calculate the elasticity of demand between the following prices. Price of crackers Quantity Demanded (per month) $3 80 $2.5 120 $2 160 $1.5 200 $1 240 $1.00 - $1.50: -0.333 $1.50 - $2.00: -0.6 $2.00 - $2.50: -1 $2.50 - $3.00: -1.66 If the price of graham crackers is $2.50 should firms raise or lower
Premium Economics Costs Microeconomics
GMB 713 PROBLEM SET NO. 2 PROBLEM SOLVING: Solve the following problems. Show all pertinent solutions. 1. A car battery dealer is trying to determine which of the brands of car battery he is selling has a longer life span. He conducted an investigation by interview his customers and was able to get the following results: Brand X Brand Y Mean life span 4.5 years 4.9 years Standard deviation
Premium Arithmetic mean Standard deviation Problem solving
PROBLEM SET # 1 Instructions: 1) Open book‚ open notes limited to only class materials. 2) Unlimited time. 3) This must be reflective of your individual effort. GMU Honor Code applies. 4) The Problem Set #1 (only the question solutions portion) is due at the end of the day on September 24th. 5) Show all work‚ as partial credit will be given for each question’s answer. Organize your work so it is easy to follow. You can use word‚ power point‚ excel or combinations
Premium Net present value Investment Bond
University of Hong Kong 1st semester 2014-15 ECON0301/ECON2252 Theory of International Trade Problem Set 1 Due time: 5pm September 26‚ 2014 (Friday) Answer all of the following questions. While I encourage you to discuss with your classmates‚ you have to write up your own script. Please hand it in to your TA (Miss Jiuqi Zhao) by the due time via her pageon box on the 9th ‡oor of K.K. Leung Building. 1. Suppose that Home and Foreign have the marginal product of labor shown below. Home Foreign Baseball
Premium Economics International trade Trade
Problem Set 1 Ben Polak‚ Econ 159a/MGT522a. Four Questions due September 19‚ 2007. 1. Strictly and Weakly Dominated Strategies? What is the de nition of a strictly dominated strategy? What is the de nition of a weakly dominated strategy? Give an example of a two-player game matrix where one player has three strategies‚ one of which is strictly dominated; and the other player has three strategies‚ one of which is weakly (but not strictly) dominated. Indicate the dominated strategies. 2. Iterative
Premium Game theory Nash equilibrium Voting