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Lecture1 - Lecture 1 Basic Concepts ECE 514 Fundamental...

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1 Lecture 1: Basic Concepts ECE 514 Fundamental notions and properties What is a random experiment? Randomness is associated with uncertainty, ignorance, etc. Ex: 1. Take an input perfectly known to you and apply it to a filter with a known impulse response. Don’t know the input? L Random? What constitutes randomness? 2. Observe a sinusoidal wave on an oscilloscope. Is it random? Why? Random Experiment Definition : A random experiment is one in which the output cannot be perfectly known from a mere knowledge of the input. Properties: A random experiment is theoretically repeatable Its output, however, cannot be predicted exactly If we cannot predict the face of a die throw, what is the next best thing? Example Example : If we throw a coin “n” times and obtain “n h heads, what can we say about the outcome heads? (Assuming n goes to infinity) n h /n = relative frequency If we can’t predict, exactly, what does the frequency tell you? Quality Assurance 1000 250 150 500 100 Tot 360 150 60 150 0 5W 200 100 0 50 50 2W 440 0 90 300 50 1W Tot. 10K 1000 100 10 P. Rat. Resistor Values Interpretation Pick a resistor at random, and try to say something about your pick. (Remark: same thing when you pick a stock, using “history,” try to “smartly” choose the right one) What are the chances (probability) that you pick a 10 W resistor? P(10 W ) = 100/1000 = 0.1 (elementary event) P(2 W) = 200/1000 = 0.2 One may want to know how likely they are at picking a 100 W and it be 2W. P(10 W , 2 W) = 50/1000= 0.05
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