ece804_ps1

# ece804_ps1 - ECE 804 Random Signal Analysis OSU Autumn 2010...

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ECE 804, Random Signal Analysis Sep. 24, 2010 OSU, Autumn 2010 Due: Oct. 4 Problem Set 1 Problem 1 For the set Ω = { 1 , 2 , 3 , 4 } , (a) Find the minimal field that contains the subsets { 1 , 2 } and { 2 , 4 } . (b) Find the minimal field that contains the subsets { 1 , 2 } and { 3 , 4 } . Problem 2 Consider the random experiment: The time until a PC fails is observed. (a) Define a sample space Ω for this experiment. (b) Describe a possible relevant choice for the field F . (c) Define two events that are mutually exclusive. (d) Define two events that have a nonempty intersection. Problem 3 A photon counter connected to the output of a fiber detects the number of photons, { N i , i > 1 } , received for successive pulses generated by a laser connected to the input of the fiber. Specify which one of the following sequences of events, { E k , k > 1 } is increasing, decreasing or none. Very briefly explain why. (a) E k = { N 1 > k } for k > 1 (b) E k = { N k = 0 } for k > 1 (c) E k = { min m 6 k N m = 0 } for k > 1 (d) E k = { max m 6 k N m > k } for k > 1 Problem 4 For a sequence of events, { E n , n > 1 } , prove the following:

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• Fall '05
• UYSAL-BIYIKOGLU
• Probability theory, mutually exclusive events, Random Signal Analysis, minimal ﬁeld, possible relevant choice

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