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Let X and X be IID Gaussian random variables with Xi~ N(0,02), i = 1,2. Let Y = X + X. Then answer the
Let X and X be IID Gaussian random variables with Xi~ N(0,02), i = 1,2. Let Y = X + X. Then answer the following questions. (a) Find the distribution of Y by using functions of random variable' approach. You can use the convolution of pdf formula if it is required. (b) Find the conditional distribution of X given Y = y. Interpret the result obtained. What will you expect the conditional distribution of X2 given Y = y to be?
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Probability and Random Processes With Applications to Signal Processing and Communications
Authors: Scott Miller, Donald Childers
2nd edition
123869811, 978-0121726515, 121726517, 978-0130200716, 978-0123869814
