1Lecture 1: Basic ConceptsECE 514Fundamental 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? LRandom?What constitutes randomness?2. Observe a sinusoidal wave on an oscilloscope. Is it random? Why?Random ExperimentDefinition:A random experimentis 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?ExampleExample:If we throw a coin “n” times and obtain “nh”heads, what can we say about the outcome heads? (Assuming n goes to infinity) nh/n = relative frequency➘If we can’t predict, exactly, what does the frequency tell you?Quality Assurance1000250150500100Tot3601506015005W200100050502W440090300501WTot.10K100010010P. Rat.Resistor ValuesInterpretation●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 Wresistor?❖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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