> Let the probability density function of the random variable X is x {2 (2) Then Mx (t) is (a) 2(3-et)-¹ (c) 2et (3-e¹)-¹ a b C f(x) = d - , x = 1,2,3,... , otherwise (b) 3(2-e¹)-¹ (d) et (3-e¹)-1
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- Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . . . , pn}. The entropyof the random variable is defined asH(X) = −Σpilog (pi) Find the probability mass function for the above discrete random variable that maximizes the entropy.f(x) = {**/3, Let X be a random variable with density function -1< x < 2, elsewhere. Find the expected value and the covariance of g(X) = 4x + 3.SOLVE STEP BY STEP IN DIGITAL FORMAT ÿ » Ü ¸♥ 286. Let X be a random variable with distribution Ber(p) and let a and b be two constants with a 0. Define the random variable Y = ax + b. find a) The probability function of Y. b) E(Y). c) Var(Y). d) E(Y) for n = 1, 2,...
- 7(1) Let X = b(16, -) find E(4-3x) and distribution function. (2) Let X be a random variable with p.d.f. -2 kx 1A random point (X,Y) is distributed uniformly on the square with vertices (1,1), on the square. (1,-1), (-1, 1), and (-1,-1). That is, the joint pdf is f(x,y) Determine the probabilities of the following events. (a) x² + y² 0 (c) |X+Y| < 22. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).Let X and Y be independent exponential random variables with parameters 2 and 3. (a) What is the probability that X + Y > 1. (b) Conditional on X + Y = 1, what is the distribution of X.n/forms/d/e/1FA WOKWy-OFrmBkWSLSfuM-c8JCYaEdyj84150 Psuod: The joint probability distribution function of a discrete random variable is f(xy) = cx'/y for x-1, 2, 3 and y-1, 4, 16. c + o Then P(2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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