Standard normal random variables

Reference no: EM131830258

We know, or else, it is not hard to prove, that if X and Y are independent standard normal random variables, then X + Y and X - Y are independent. This problem is devoted to a converse. Suppose that X and Y are independent symmetric random variables with mean 0 and variance 1, such that X + Y and X - Y are independent. Let ? denote the common characteristic function of X and Y. Prove, along the following path, that X and Y must be standard normal random variables:

(a) Prove that ?(2t)=(?(t))⁴.

(b) Iterate.

Reference no: EM131830258

Questions Cloud

Distribution to the standard normal distribution : Show that the central limit theorem cannot be extended to convergence in probability, that is, if X1, X2, ... are independent, identically distributed random

Most government lotteries pay out jackpots : Most government lotteries pay out jackpots in form of 20, or 30 year annuities but they also give winners option to much smaller payout to collect their winning

Distributed random variables with mean : Suppose that X and Y are independent, identically distributed random variables with mean 0 and variance 1, such that

Prepare the company cash budget for june in good form : Prepare the company's cash budget for June in good form. Make sure to indicate what borrowing, if any, would be needed to attain the desired ending cash balance

Standard normal random variables : Prove, along the following path, that X and Y must be standard normal random variables:

How much would it be willing to lend the business owner : how much would it be willing to lend the business owner?

Experiment with success probability : Consider an experiment with success probability p. The entropy is

Mutually exclusive projects : Assume Project K and Project W are mutually exclusive projects with a WACC = 10%. Which of the following is true?

Describe how you can increase consumer participation : Describe how you can increase consumer participation in the planning, implementation and evaluation of the care you deliver.

User Account

All Pages