S2017_STA_Lecture_03.pptx

S2017_STA_Lecture_03.pptx - FACULTY OF INFORMATION...

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Ta Quang Hung, Ph.D. FACULTY OF INFORMATION TECHNOLOGY Probability & Statistics Spring, 2017 Lecture 3: Random Variables & Distributions – Part 1
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Lecture 3 Probability & Statistics Contents Page 2 1 Random Variables 4 Summary 3 Continuous Distributions 2 Discrete Distributions
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Lecture 3 Probability & Statistics 1. Definition of a Random Variable 2. Distribution of a Random Variable 3. Discrete Distributions 4. Uniform Distributions on Integers 5. Binomial Distributions Page 3 RANDOM VARIABLES & DISCRETE DISTRIBUTION
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Lecture 3 Probability & Statistics A random variable can be thought of as being generated from a function that maps each outcome in a sample space onto the real number line R, as illustrated in the Figure. Definition of Random Variables A random variable is obtained by assigning a numerical value to each outcome of a particular experiment. Page 4
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Lecture 3 Probability & Statistics Definition of Random Variables Example 1 : The sample space for the machine breakdown problem is = {electrical, mechanical, misuse} and each of these failures may be associated with a repair cost. For example, suppose that electrical failures generally cost an average of $200 to repair, mechanical failures have an average repair cost of $350 , and operator misuse failures have an average repair cost of only $50 . These repair costs generate a random variable cost, as illustrated in the Figure, which has a state space of {50, 200, 350} . Page 5 Cost is a random variable because its values 50, 200, and 350 are numbers. The breakdown cause, defined to be electrical, mechanical, or operator misuse, is not considered to be a random variable because its values are not numerical.
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Lecture 3 Probability & Statistics Definition of Random Variables Example 2 : Recall the “power plant operation” example. Suppose that interest is directed only at the number of plants that are generating electricity. This creates a random variable
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  • Spring '18
  • Probability theory, New South Wales

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