# ps1 - ECE 804, Random Signal Analysis OSU, Autumn 2009...

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ECE 804, Random Signal Analysis Sep. 28, 2009 OSU, Autumn 2009 Due: Oct. 5, 2009 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)

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## ps1 - ECE 804, Random Signal Analysis OSU, Autumn 2009...

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