interval (0‚1); b) if f(x)= 2e-2x U(x) Q 4-7‚ Show that if the uniform variable x has an Erlang density with n=2‚ then Fx(x) = (1-e-cx-cxe-cx) U(x) Q 4-8‚ The random variable x is N (10; 1)‚ Find f (x | (x-10)2 <4) Q 4-9‚ Find f(x) if F(x) = (1-e-ax) U(x-c). Q 4-10‚ If x is N (0‚ 2) find a) P{1≤ x ≤ 2} b) P{1≤ x ≤2 | x ≥ 1} Q4-14‚ A fair coin is tossed 900 times and the random variable x equals the total number of heads. a) Find fx(x)‚ 1: exactly‚ 2: approximately
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(ISOM2500)[2012](f)midterm1~=0zvopee^_78631.pdf downloaded by mhwongag from http://petergao.net/ustpastpaper/down.php?course=ISOM2500&id=0 at 2013-12-16 02:44:12. Academic use within HKUST only. Business Statistics‚ ISOM2500 (L3‚ L4 & L5) Practice Quiz I 1. The following bar chart describes the results of a survey concerning the relevance of study to present job by school. Focus on the School of Business and Management. What are the mode and the median respectively? (a) Relevant‚ Neutral (b) Relevant
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I. Introduction Arrowmark Vending has the contract to supply pizza at football games for a university. The operations manager‚ Tom Kealey‚ faces the challenge of determining how many pizzas to make available at the games. We have been provided with demand distributions for pizza based on past experience and know that Tom will only supply plain cheese and pepperoni and cheese combo pizzas. We also know that there is a fixed cost of $1‚000 allocated equally between the two types of pizzas‚ and that
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Random Variable and Its Probability distribution “A random variable is a variable hat assumes numerical values associated with the random outcome of an experiment‚ where one (and only one) numerical value is assigned to each sample point”. “A random variable is a numerical measure of the outcome from a probability experiment‚ so its value is determined by chance. Random variables are denoted using letters such as X‚Y‚Z”. X = number of heads when the experiment is flipping a coin 20 times. There
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are lifted at a time. Compute the probability of an accident. [0.1587] 3. A soft –drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 milliliters and a standard deviation of 15 milliliters. What is the probability that the mean amount dispensed in a random sample of size 36 is at least 204 milliliters? [0.0548] 4. An automatic machine in a manufacturing process is operating properly if the lengths of an important
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EE 562a: Random Processes in Engineering EE department‚ USC‚ Fall 2014 Instructor: Prof. Salman Avestimehr Homework 1 Solutions 1. (Axioms of Probability) Prove the union bound: n P [∪n Ak ] ≤ k=1 P [Aj ]. j=1 The union bound is useful because it does not require that the events Aj be independent or disjoint. Problem 1 Solution We prove this part by induction‚ for k = 2 we have P (A1 ∪ A2 ) = P (A1 ) + P (A2 ) − P (A1 ∩ A2 ) ≤ P (A1 ) + P (A2 ) (1) Now‚ assume that
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ISSN 1995-0802‚ Lobachevskii Journal of Mathematics‚ 2009‚ Vol. 30‚ No. 4‚ pp. 337–346. c Pleiades Publishing‚ Ltd.‚ 2009. Marcinkiewicz-Zygmund Type Law of Large Numbers for Double Arrays of Random Elements in Banach Spaces Le Van Dung1* ‚ Thuntida Ngamkham2 ‚ Nguyen Duy Tien1** ‚ and A. I. Volodin3*** 1 Faculty of Mathematics‚ National University of Hanoi‚ 3 34 Nguyen Trai‚ Hanoi‚ Vietnam 2 3 Department of Mathematics and Statistics‚ Thammasat University‚ Rangsit Center‚ Pathumthani
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Rapid Surveys (unpublished)‚ © 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling‚ but few use this method for population-based surveys. Rapid surveys are no exception‚ since they too use a more complex sampling scheme. So why should we be concerned with simple random sampling? The main reason is to learn the theory of sampling. Simple random sampling is the basic selection process of sampling and is easiest to understand
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Types of Variables Binary variable Obsevations (i.e.‚ dependent variables) that occur in one of two possible states‚ often labelled zero and one. E.g.‚ “improved/not improved” and “completed task/failed to complete task.” Categorical Variable Usually an independent or predictor variable that contains values indicating membership in one of several possible categories. E.g.‚ gender (male or female)‚ marital status (married‚ single‚ divorced‚ widowed). The categories are often assigned numerical
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THE MOMENTS OF A RANDOM VARIABLE Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as Mk (X) = E[ (X c)k ]. (12) In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k‚ i.e.‚ k = E(Xk )‚ where c = 0 has been inserted into equation (12). Moments about the
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