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- Simplify the following Boolean functions, using K-maps: F (A, B, C, D)=Σ(4, 6, 7, 15)Let X1, X2, .,X25 be i.i.d. random variables from Po(5). Estimate the MSE for the median estimator using Monte Carlo estimation.In a normal distribution: The shape of the distribution is ["", ""] , the dispersion is ["", "", ""] , and the peaks are described as ["", "", ""] .
- Let X be discrete random variable. If P(XUsing the MATLAB Histogram function, "hist.m", Illustrate the Central Limit Theorem by taking two different random variables and show how when appropriately scaled and summed, they converge to a Normal (Gaussian) distribution.4. Given a random variable w with den sity F(w) and a random variable p as the umiform im the interval (-71, +71) where wlP (two w and p are independent) R.V.S Suppose the stochastic process, xt) =a Cos (wt+P). meam a) show that xlt) is wss with zero and auto correlation equal R(E) = E (Coswr) j(wt+P) b) show that zt)=aé is also a Wss.
- Let X be a random variable with density function 1) ={0. k(1 -x), if 0<*<1; otherwise. f(x) Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1.Please explain, as simplistically (but thoroughly) as possible, how to develop a k-map from a truth table to be used to simplify an equation.Examples: xz + (xy + ~z) ~xyz + yz + x~yBoolean function is represented by its truth table as follows: хуz f(x,y,z) 000 1 001 1 010 011 100 101 1 110 111 1 (a) Write corresponding minterm expansion. (b) Write corresponding maxterm expansion. (c) Minimize (Simplify) and Represent f(x,y,z) using Karnaugh map (K-map). (d) Minimize (Simplify) f(x,y,z) using Boolean identities. (e) Represent the simplified function using logic diagram.