Let , be independent N(0,1) distributed random variables. Define and . Without using calculus, show that .
Let , be independent N(0,1) distributed random variables. Define and . Without using calculus, show that...
Let be independent, identically distributed random variables with . Let and for , . (a) Show that is a martingale. (b) Explain why satisfies the conditions of the martingale convergence theorem (c) Let . Explain why (Hint: there are at least two ways to show this. One is to consider and use the law of large numbers. Another is to note that with probability one does not converge) (d) Use the optional sampling theorem to determine the probability that ever attains...
Let , ... be independent random variables with mean zero and finite variance. Show that We were unable to transcribe this imageWe were unable to transcribe this image
Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following is sucient to conclude that the estimator T = f(X1,...,Xn) of a parameter ✓ is consistent (fully justify your answer): (a) Var(T)= (b) E(T)= and Var(T)= . (c) E(T)=. (d) E(T)= and Var(T)= We were unable to transcribe this imageWe were unable to transcribe this imageoe We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Let X1,X2,...,Xn denote independent and identically distributed random variables with mean µ and variance 2. State whether each of the following statements are true or false, fully justifying your answer. (a) T =(n/n-1)X is a consistent estimator of µ. (b) T = is a consistent estimator of µ (assuming n7). (c) T = is an unbiased estimator of µ. (d) T = X1X2 is an unbiased estimator of µ^2. We were unable to transcribe this imageWe were unable to transcribe...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ We were unable to transcribe this image
Let be independent random variables, where ~, Is sufficient for ? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagePoi(ix) 2 We were unable to transcribe this imageWe were unable to transcribe this image
Let be independent random variables, where ~, . Find a sufficient statistics for . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageuni form(i) We were unable to transcribe this imageWe were unable to transcribe this image
Let be independent random variables, where ~, Find a sufficient statistic for . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
e (4 marks) Let m be an integer with the property that m 2 2. Consider that X1, X2,.. ., Xm are independent Binomial(n,p) random variables, where n is known and p is unknown. Note that p E (0,1). Write down the expression of the likelihood function We assume that min(x1, . . . ,xm) 〈 n and max(x1, . . . ,xm) 〉 0 5 marks) Find , and give all possible solutions to the equation dL dL -...
Given two independent random variables and and a function and given that , does the following inequality hold? I have tried doing it this way. Now, because and are independent, Is my approach correct? We were unable to transcribe this imageWe were unable to transcribe this imagef(X) We were unable to transcribe this imageax{f(E[X1]), f (E[X2)}<a 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
Post an Article
Post an Answer
Post a Question
with Answer
Self-promotion: Authors have the chance of a link back to their own personal blogs or social media profile pages.