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# final - ECE-340 Spring 2010 Final Examination May 10th 2010...

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1 ECE-340, Spring 2010 Final Examination, May 10 th , 2010; 5:30-7:30 PM 1. Suppose that there are two categories of eggs: large eggs and small eggs, occurring with probabilities 0.7 and 0.3, respectively. For a large egg, the probabilities of having 1, 2, or 3 yolks are 0.95, 0.045 and 0.005, respectively. On the other hand, for a small egg, the probabilities of having 1, 2, or 3 yolks are 0.98, 0.019 and 0.001, respectively. Suppose that an egg is picked at random and let X represent the number of yolks in it. a) Plot the cumulative distribution function of X . b) Calculate the mean and variance of X . c) Suppose that it is known that an egg has more than one yolk, what is the probability that is has three yolks? d) Suppose that it is known that an egg has three yolks, what is the probability that it is a large egg?

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2 2. Consider the RC circuit shown below. Suppose that the noisy resistor is at temperature T Kelvin and its noise is modeled as Johnson noise.
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