First Problem Assignment EECS 401 Due on January 12‚ 2007 PROBLEM 1 (15 points) Fully explain your answers to the following questions. (a) If events A and B are mutually exclusive and collectively exhaustive‚ are Ac and Bc mutually exclusive? Solution Ac ∩ Bc = (A ∪ B)c = Ωc = ∅. Thus the events Ac and Bc are mutually exclusive. (b) If events A and B are mutually exclusive but not collectively exhaustive‚ are Ac and Bc collectively exhaustive? Solution Let C = (Ac ∪ Bc )c ‚ that is the
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TRIDENT UNIVERSITY INTERNATIONAL Done By: Course # MAT201 Case Module 1 Introduction of Probability Instructor: 1. In a poll‚ respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected‚ what is the probability of getting someone who has traveled to Europe? Outcome: selecting someone who has been
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probability theory which is often refereed to as the science on uncertainty” (Lind‚ Marchal‚ & Wathen‚ 2008). This is the number that explains the chance that something will happen. “Probability is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty)‚ also expressed as a percentage between 0 and 100%” (Math World‚ n.d.). There are two ways to appoint
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heart attack. If the patient survives the surgery‚ he has a 50% chance that the heart damage will heal. Find the probability that the patient survives and the heart damage heals. Let BS be the event that the patient survives bypass surgery. Let H be the event that the heart damage will heal. Then P(BS) = 0.60‚ and also we have a conditional probability: given the patient survives the probability that the heart damage will heal is 0.5‚ that is P(H|BS) = 0.5
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Probability theory Probability: A numerical measure of the chance that an event will occur. Experiment: A process that generates well defined outcomes. Sample space: The set of all experimental outcomes. Sample point: An element of the sample space. A sample point represents an experimental outcome. Tree diagram: A graphical representation that helps in visualizing a multiple step experiment. Classical method: A method of assigning probabilities that is appropriate when all the experimental
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handle Dependent Events Life is full of random events! You need to get a "feel" for them to be a smart and successful person. Independent Events Events can be "Independent"‚ meaning each event is not affected by any other events. Example: Tossing a coin. Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. The chance is simply 1-in-2‚ or 50%‚ just like ANY toss of the coin. So each toss is an Independent Event. Dependent Events But events can also
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experiment. (b) Describe a possible relevant choice for the field F . (c) Define two events that are mutually exclusive. (d) Define two events that have a nonempty intersection. Problem 3 A photon counter connected to the output of a fiber detects the number of photons‚ {Ni ‚ i 1}‚ received for successive pulses generated by a laser connected to the input of the fiber. Specify which one of the following sequences of events‚ {Ek ‚ k 1} is increasing‚ decreasing or none. Very briefly explain why. (a) Ek
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activity is required to think of every possible cost would be happened in the process of delivering an event. Budgeting is to deal with the financial management applying the financial tools and techniques. It is significantly to make decision on each segment‚ such as staff‚ venue‚ to ensure the resource is efficiency to use. 2. Briefly define three of the following concepts in the context of event design/theming - balance‚ emphasis‚ design‚ harmony‚ rhythm and proportion. Proportion is a connection
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I. Probability Theory * A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs‚ but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. * The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation
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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 the statement is true for k = n n P (A1 ∪ A2
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