Lecture2_RandomExperiments

# Lecture2_RandomExper - ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Lecture 2 Random Experiments Prof Vince Calhoun Reading This class

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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 2: Random Experiments Lecture 2: Random Experiments

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Reading • This class: Section 2.1-2.2 • Next class: Section 2.3-2.4 • Homework: • Assignment 1: From the text, problems 2.1, 2.2, 2.3, 2.5, 2.9 • Due date: Monday Feb. 4 at the beginning of class.
Outline • Section 2.1 • Examples of experiments •D i s c r e t e • Continuous •E v e n t s E x a m p l e s • Certain event • Null event • Set Operations • Union

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A phenomenon is random if individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions. Randomness and probability The probability of any outcome of a random phenomenon can be defined as the proportion of times the outcome would occur in a very long series of repetitions.
Coin toss The result of any single coin toss is random. But the result over many tosses is predictable, as long as the trials are independent (i.e., the outcome of a new coin toss is not influenced by the result of the previous toss). The result of any single coin toss is random. But the result over many tosses is predictable, as long as the trials are independent (i.e., the outcome of a new coin toss is not influenced by the result of the previous toss). First series of tosses Second series The probability of heads is 0.5 = the proportion of times you get heads in many repeated trials.

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Probability models mathematically describe the outcome of random processes. They consist of two parts: 1) S = Sample Space: This is a set, or list, of all possible outcomes of a random process. An event is a subset of the sample space. 2) A probability for each possible event in the sample space S. Probability models Example: Probability Model for a Coin Toss S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5

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Important: It’s the question that determines the sample space. Sample space A. A basketball player shoots three free throws. What are the possible sequences of hits (H) and misses (M)? S = {HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM } B. A basketball player shoots three free throws. What is the number of baskets made? S = {0, 1, 2, 3} C. A person tosses one coin and rolls one die. What are the possible combined outcomes? S = {H1, T1, H2, T2, H3, T3, H4, T4, H5, T5, H6, T6}
In some situations, we define an event as a combination of outcomes. In that case, the probabilities need to be calculated from our knowledge of the probabilities of the simpler events. Example: You toss two dice. What is the probability of the outcomes summing

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## This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture2_RandomExper - ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Lecture 2 Random Experiments Prof Vince Calhoun Reading This class

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