2017sp_ECE353_HW1_Solution

2017sp_ECE353_HW1_Solution - ECE 353 Introduction to...

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ECE 353: Introduction to Probability and Random Signals - Spring 2017 Homework 1 Solution 1. Consider the experiment of placing three distinguishable particles a, b, and c into three cells. Examples of sample points are 1 | | abc   , 2 | | ab c , etc. a. Write down the sample space . | | , | | , | | , | | , | | , | | | | , | | , | | , | | , | | , | | | | , | | , | | , | | , | | , | | | | , | | , | | , | | , | | , | | | | , | | , | a b c a c b b a c b c a c a b c b a ab c ab c c ab ab c c ab c ab ac b ac b b ac ac b b ac b ac bc a bc a a bc bc a a bc a bc abc abc     | abc b. Define events as: multiple particles occupy a cell the last cell is not empty A occurs but not B. A B C Write down the sample points in events A , B , and C respectively. | | , | | , | | , | | , | | , | | | | , | | , | | , | | , | | , | | | | , | | , | | , | | , | | , | | | | , | | , | | | | , | | , | | ab c ab c c ab ab c c ab c ab ac b ac b b ac ac b b ac b ac A bc a bc a a bc bc a a bc a bc abc abc abc a b c a c b b a c B
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