Let X, X,...X, be 'n' random variable which are identically distributed such that Xg= 1 with a prob. of 1/2 = 2 with a prob. of 1/3 =-1 with a prob. of 1/6. Find (a) E [X, + X2 +... .. X,1 (b) E [X} + X3 +...X
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- A random walk (RW) {Sn}n>o is a sum of id r.v.s X1, X2, •• , Xn,withP(X1 = a) = p, P(X1 = b) = 1 -p= q.Find the expectation E(Snl and variance var(Sn) of Sn for any n.(1) Let X be a random variable with p.d.f. 1-8x 0Prove the followingQ2/(a) Let Xbe a random variable with p.d.f. 19. If X and Y are two random variables and let g(X) be a random variable. Show that (a) E[g(X) X=x] = g(x). (b) E[g(x)Y|X=x] = g(x) E[Y|X=x]. Assume that E[g(x)] and E[Y] exist.Suppose X is a random variable such that E(X) = 90 and Var(X) = 7. Compute thefollowing: E(4X + 12) Var(−X) SD(4X)E(X^2) E(X + 3)^2SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON