The PMF of a random variable X is given by: P(X - 0) 0.15 P(X = 1) P(X = 2) 0.35 0.50 Find the average information (entropy) in bits represented by X
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- For a random variable X E(X) = 1.27, E(X²) = 3.79 The variance of X is equal to Select one: O 2.52 O 2.9843 O 2.1771 O 0.758 0.3351Three statistically independent random variables X₁, X₂ and X₂ have mean values X₁ =3, X₂ = 6 and X₂ = -2. Find the mean values of the following functions: 1 2 (a) (b) g(X₁, X₂, X3)= X₁ +3X₂ + 4X3 29 g(X₁, X₂, X3) = X₁X₂X₂ 29Show all solution The pmf of a discrete random variable X is as follows: X -1 0 1 2 f(x) 1/10 2/10 5/10 2/10 Use this pmf to evaluate the following: mean of X variance of X
- rom the set of numbers {4,6, 8}, a random sample of size 2 is selected with replacement. (a) Determine the sampling distribution of the sample mean X. (b) Find the mean E(X) of the sampling distribution of the sample mean X. Compare E(X) with the population mean u.A random variable takes the values 1, 2, 3 where P(x-1)%3D0.5 and E(x)=1.7, then P(x >2]X>1)=D O a. 0.2 O b. 0.8 O .1 O d. 0.4P(-0.34The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(0Let X be the random variable with PMF: p(x) = k(]x – 2|+ 1), for x= -2, -1, 0, 1, 2 0, elsewhere (a) Find the value of k (b)Find the PMF of X (c) Find the mean, variance, and the standard deviation of XHand write， As soon as possibleSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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