The random variable Y with density 1 fy)={v+n² y>0, |0, y<0. Develop a pseudo-code algorithm for generating random variate using inverse transformation method.
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- Suppose Y₁,..., Yn are independent random variables each with the Pareto distribution and E(Y) = (Bo + B1Xi) Is this a generalized linear model with a canonical link? Give reasons for your answer.Find auto-correlation function of a random process whose power spectral densis is given by 1+. 4Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?
- Please solve with the step max in 60-90 minutes the chapter actuarial Investigate whether the risk measure Variance principle premium p(L) = μL + ασL2 α = loading factor meets the axioms (T, S, PH and M)2 If X₁ and X₂ are the means of independent ran- dom samples of sizes n₁ and n₂ from a normal population with the mean u and the variance o2, show that the vari- ance of the unbiased estimator 2 w X₁ + (1-w). X₂ is a minimum when @ = n1 n₁ + n₂ idnuLet Y₁, Y2, Y3, Y₁, Y5 be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁² + Y₂² + 3Y3²+ Y₂² +4Y5² Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X2,..., X, be independent and normally distributed random samples from populations with means ₁ = 2 and ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of 0₂² = k.
- Explain these tables and what is the difference between the first table of t-test and the second table of t-testA 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 answersirDefine Least Squares Regression Unbiased Estimators α^, β^, σ^²?
- 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 certainProve that b is an unbiased estimator for ß. What are the essential conditions to prove ordinary least squares (OLS) estimator is unbiased? E(b) = ßHeteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…