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EE 560 Week 2 Homework Problems

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EE560 week 2 homework problems Chapter 3: Problem 3.1.) Let X be the maximum of the number of heads obtained when Carlos and Michael each flip coin twice. a.) Describe the underlying space S of this random experiment and specify the probabilities of its elementary events. Problem 3.2.) A die is tossed and the random variable X is defined as the number of full pairs of dots in the face showing up. Problem 3.3.) The loose minute hand of a clock is spun hard. The coordinates (x,y) of the point where the tip of the hand comes to rest is noted. Z is defined as the sgn function of the product of x and y, where sgn(t) is 1 if t>0, 0 if t=0, and -1 if t<0. Problem 3.5.) Two transmitters send messages through bursts of radio signals to an antenna. During each time slot each transmitter sends a message with probability ½. Simultaneous transmissions result in loss of the message. Let X be the number of time slots until the first message gets through. Chapter 9: Problem 9.2.) A discrete-time random process X is defined as follows. A fair die is tossed and the outcome k is observed. The process is then given by X =k for all n. Problem 9.3.) A discrete-time random process X is defined as follows. A fair coin is tossed. If the outcome is heads, X = (-1)^n for all n; if the outcome is tails, X = (-1)^(n+1) for all n Problem 9.5.) Let g(t) be the rectangular pulse shown in Fig. P9.1. The random process X(t) is defined as Problem 9.7.) A random process is defined by

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EE560 week 2 homework problems Chapter 3: Problem 3.1.) Let X be the maximum of the number of heads obtained when Carlos and Michael each flip coin twice. a.) Describe the underlying space S of this random experiment and specify the probabilities of its elementary events. Problem 3.2.) A die is tossed and the random variable X is defined as the number of full pairs of dots in the face showing up. Problem 3.3.) The loose minute hand of a clock is spun hard. The coordinates (x,y) of the point where the tip of the hand comes to rest is noted. Z is defined as the sgn function of the product of x and y, where sgn(t) is 1 if t>0, 0 if t=0, and -1 if t<0. Problem 3.5.) Two transmitters send messages through bursts of radio signals to an antenna. During each time slot each transmitter sends a message with probability ½. Simultaneous transmissions result in loss of the message. Let X be the number of time slots until the first message gets through. Chapter 9: Problem 9.2.) A discrete-time random process X is defined as follows. A fair die is tossed and the outcome k is observed. The process is then given by X =k for all n. Problem 9.3.) A discrete-time random process X is defined as follows. A fair coin is tossed. If the outcome is heads, X = (-1)^n for all n; if the outcome is tails, X = (-1)^(n+1) for all n Problem 9.5.) Let g(t) be the rectangular pulse shown in Fig. P9.1. The random process X(t) is defined as Problem 9.7.) A random process is defined by

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