A xondom Variable x takes value X; with Probabilty Pi, with i = 1,... N labelling all possibilities. The meon Value of X is given, And Shonon entropy of x S(x) = H1 N i=1 is it It N ≤ Pixi - given as, Z PilogPi i=1 chu

Q: For each n ≥ 1, take An= (-1/n, 1/n). Then, 1 An {0} and U1 An (-1, 1). Prove these.

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Q: x-1 Given p(x) = (.33)(.67)^', x = 1, 2, 3... %3D Find p(2). O A. .7789 о в. 2211 О с. 33 D. none of…

A: Let X be the random variable having probability mass function is,  P(X) = (0.33)*(0.67)x-1 ,     x =…

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A: As per our guidelines we are suppose to answer only three subparts kindly post theremaining subparts…

Q: 4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and…

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Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: Let X follows exponential with lambda=4. The sample of size 4 was drawn. Find P(X1’ 1)

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Q: 3. Entropy is also defined when classification is into three or more classes. The entropy of a set S…

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Q: 0.90 HW 3: If Z- N(0.1). find a such that (a) P(Za) 0.25 0.25

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Q: Q. 4 Let X be uniform on [0, a] with a > 0, and define the event B = {X > b} such that 0 < b < a.…

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Q: 2. A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the…

A: Given: X=-2,-1,0,1,2 Y=X±1 Here possible pairs of x,y=-2,-1,-2,-2, has totally 5×3=15. Joint PMF of…

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Q: 3.7.2 WP Suppose that X has a hypergeometric distribution with N = 10, n = 3, and K = 4. Sketch the…

A: Solution Given, N=10, n=3, K=4

Q: I For each, compute the value ,or show diseryont" (abte machinteyml i "impropar!) A = e^e 2. 2x+1 B…

A: I : For each compute the value or show divergent.  NOTE: Each integral is improper The given…

Q: 4. The joint p.d.f. f(x1, x2, x3) is constant over the cube S. Since .1 dæ1 dæ2 dr3 = dæ1 dx2 dx3 =…

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Q: 1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric…

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A: Introduction: The Alternating Series Error Bound Theorem is a mathematical theorem that…

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Q: 2. A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the…

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Q: We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the…

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Q: Let be a particular value of x. Find the value of x such that the following is true. .P(x>x) =0.05…

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Q: Let x~ gamma Ca,ß) ASsum a = 4 B = 3 Find © P { I x-MI >204 Pfix-MIS 307

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Q: Show that YN = Nỹn is unbiased for Yy. That is, show that E[ YN]= YN -

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Q: distributed random variables with Var(X1) < . Show that 1 n(n +1) jX; →, EX1. j=1 Note. A simple way…

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Q: Let f(x) = 1+ x² + x4 + •…+ x²k (k € Z+ u {0}). For what value of k, 23 mean value of f (x) is on…

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