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Let X and Y be independent exponential random variables with parameter 1. Find the cumulative
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- please and thank you!!!Using XTWX for information matrix show the variance of the MLE of beta in logistic regression is 1/a +1/b+1/c+1/d where outcome no outcome exp a b not exp c dLet 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.
- A random process Y(t) is given by Y(t)= Acos(wt+F) where w is a constant, and A and F are independent random variables. The random variable A has a mean of 3 and a variance of 9, and F is uniformly distributed between -p and p. Determine if the process is a mean-ergodic proces Please tapy answersirLet X₁, X2, X3, Xn be a random sample with unknown mean EX; = µ, and unknown variance Var(X₂) = o². Suppose that we would like to estimate 0 = μ². We define the estimator as 2 • - (™)² - [ 2x]* Xk to estimate 0. Is an unbiased estimator of ? Why?f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.
- Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certainThe information associated with the maximum likelihood estimator of a parameter 0 is 4n, where n is the number of observations. Calculate the asymptotic variance of the maximum likelihood estimator of 20 . (A) (В) (C) (D) 8n (E) 16nIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.
