(i) Let X be a random variable taking on the values – 1 and 1, each with probability 1/2. Find E(X) and E(X'). (ii) Now let X be a random variable taking on the values 1 and 2, each with probability 1/2. Find E(X) and E(1/X). (iii) Conclude from parts (i) and (ii) that, in general, E[g(X)] + g[E(X)] for a nonlinear function g(-). (iv) Given the definition of the F random variable in equation (B.43), show that E(F) = E [(X/k2). Can you conclude that E(F) = 1?

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Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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Q: (51) Let X be a random variable with p.d.f. 2e-2x 0<x<00 = (x) , find E(e") O.w

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Q: Let X be a random variable with p.d.f. x = 1,2,3 f(x) = { find (1) k (2) E(x²) O.W

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Q: We have a random variable X, withE(X) = {5, 2, 10), Px (5) = 1/3.Px (2) = 1/6 et Px (10) = 1/2. We…

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Q: (41) Let X be a random variable with p.d.f. [(k+4) 0<x<5 ,find (1) k (2) E(x +1) (x) O.w

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Q: Let X be a random variable with p.d.f. 2e-2x f(x)=< 0<x<0 , find E(e2") O.w

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A: Given as,  Xi follow exponential with mean λ.

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