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Variables Mardan Marks : 50 Special Assignment Course Code: EE-202 Course title: Probability and Random Department of Electrical Engineering UET Note: Attempt all the given questions. Justify each step. Show all the steps of your work in detail. Q1. [Marks:10] In case X and Y are independent variables how do you discover the matrix (table) representing from its margins? Q2. [Marks:10] A signal s=3 from a satellite but is corrupted by noise and the received signal is ,when the weather is good which happens with probability 2/3,W is a normal (Gaussian) random variable with zero mean and variance 9.in the absence of any weather information : (a). Examine the p.d.f of X using total probability theorem. (b). List all the probabilities that X is between 2 and 4. Q3. [Marks :20] (a). Let X and Y are continuous random variables and they are correlated. Inspect their independence. (b). Let X and Y are independent and discrete random variables. Examine their un correletedness. (c). Suppose that X and Y are discrete random variables. X is uniformly distributed between -1 and 1 and let Examine the uncorreletedness and not independentness of X and Y, Also conclude that E(Y/ X=0). Q4. [Marks :10] Two r.v. x and y are uncorrelated if = E[(x - )(y-) = 0 or equivalently Rxy = E[x = E[x]E[] = White random vector : This is defined to be a r.v. with zero mean and unit covariance (correlation) matrix. Rx = Cx = I Discover the mean and covariance of the white random variable under the orthogonal transform. 1| Page