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- Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also Var(X + Y) = Var(X) + Var(Y) true.Please show steps to find solution for markov chainSuppose that X₁, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x)=12* for x ≥ 0 and Fx (x) = 0 for x 4).
- Suppose that X1, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x) = 1 – 2 for x >0 and Fx (x) = 0 for x 1).Let X be a random variable with sample space {1,2, 3} and probability distribu- (G 1 ). Find a transition matrix P such that the Markov chain {X„} tion T = simulates X.Let X be a Poisson random variable with mean λ = 20. Estimate the probability P(X ≥25) based on: (a) Markov inequality. (b) Chebyshev inequality. (c) Chernoff bound. (d) Central limit theorem.
- Show by example that chains which are not irreducible may have many different stationary distributions.Let X, X2,..., Xg be i.i.d random variables from a distribution with p.d.f co"e , z>0 otherwise, f(r) = where c is a constant that makes this a valid p.d.f.. Let Y=YX². Use Markov's inequality to find an upper bound for P(Y > 1260).Suppose that X₁, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x) = 1 – 3¯ª for x ≥ 0 and Fx (x) = 0 for x 1).
- The index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails, |, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail, is V than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.)Suppose X₁, X2, ..., X₁ are independent random variables and have CDF F(x). Find the CDF of Y = min{X₁, X₂,, Xn} and Z = max{X₁, X₂, ···‚ Xn}.