UCSD ECE 287 A Handout
نویسنده
چکیده
(a) H(X|Z) vs. H(X|Y ) +H(Y |Z). (b) h(X + Y ) vs. h(X), if X and Y are independent continuous random variables. (c) h(X + aY ) vs. h(X + Y ), if Y ∼ N(0, 1) is independent of X and a ≥ 1. (d) I(X;Y ) vs. I(X1;Y1) + I(X2;Y2), if p(y |x) = p(y1|x1)p(y2|x2). (e) I(X;Y ) vs. I(X1;Y1) + I(X2;Y2), if p(x ) = p(x1)p(x2). (f) I(aX + Y ; bX) vs. I(X + Y/a;X), if Y ∼ N(0, 1) is independent of X and a, b 6= 0. 4. Maximum differential entropy. Let X ∼ f(x) be a zero-mean random variable and X ∼ f(x) be a zero-mean Gaussian random variable with the same variance as X.
منابع مشابه
UCSD ECE 250 Handout # 18
(a) Find P{X10 = 10}. (b) Approximate P{−10 ≤ X100 ≤ 10} using the central limit theorem. (c) Find P{Xn = k}. 2. Absolute-value random walk. Consider the symmetric random walk Xn in the previous problem. Define the absolute value random process Yn = |Xn|. (a) Find P{Yn = k}. (b) Find P{max1≤i<20 Yi = 10 |Y20 = 0}. 3. A random process. Let Xn = Zn−1 + Zn for n ≥ 1, where Z0, Z1, Z2, . . . are i....
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تاریخ انتشار 2008