# Question: Suppose X1 X2 Xn is a sequence of IID positive

Suppose, X1, X2, Xn, is a sequence of IID positive random variables. Define

Show that as n →∞, yn converges in distribution, and find the distribution to which it converges.

Show that as n →∞, yn converges in distribution, and find the distribution to which it converges.

## Relevant Questions

Let Xk, k = 1, 2, 3… be a sequence of IID random variables with finite mean, , and let Sn be the sequence of sample means, (a) Show that the characteristic function of Sn can be written as (b) Use Taylor’s theorem to ...Independent samples are taken of a random variable X. If the PDF of X is uniform over the interval [–1 / √12, 1 / √12) and zero elsewhere, then approximate the density of the sample mean with a normal density, assuming ...The noise level in a room is measured n times. The error Ɛ for each measurement is independent of the others and is normally distributed with zero- mean and standard deviation σe = 0.1. In terms of the true mean, μ, ...A gambler plays a game of chance where he wins $ 1 with probability ρ and loses $ 1 with probability 1–p each time he plays. The number of games he plays in an hour, N, is a random variable with a geometric PMF, PN( n) = ...A sequence of random variables, Xn, is to be approximated by a straight line using the estimate, Ẋ n = a+ bn. Determine the least squares (i. e., minimum mean squared error) estimates for a and b if samples of the sequence ...Post your question