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Homework_5 - ECE600 Random Variables and Waveforms Spring...

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g 1 ( x ) x c -c a b -a -b 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 x g 2 ( x ) Figure 1 Figure 2 -b -a ECE600 Random Variables and Waveforms Mark R. Bell Spring 20 1 1 MSEE 336 Homework Assignment #5 Should be completed by Session 15 Reading Assignment: Reread Sections 5-1 and 5-2, and read Sections 5-3 through 5-5 of Papoulis. 1. Papoulis 5-2. 2. Papoulis 5-3. 3. Papoulis 5-4. 4. Papoulis 5-7(a). 5. Papoulis 5-9. 6. Papoulis 5-11. 7. Let X be a Gaussian random variable with mean µ = 1 and standard deviation σ = 1. Let g 1 ( x ) be the function shown in Fig. 1 below. Define a new random variable Y = g 1 ( X ). Find expressions for the cdf F Y ( y ) and the pdf f Y ( y ), and sketch them. 8. Let X be an exponential random variable with pdf f X ( x ) = e x · 1 [0 , ) ( x ) . Let g 2 ( x ) be the function shown in Fig. 2 below. Define a new random variable Y = g 2 ( X ). Find expressions for the cdf F Y ( y ) and the pdf
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