Instances of an important theorem

Reference no: EM13993193

Let Xn denote the mean of a random sample of size n from a distribution that has p.d.f. f( x) = e-x, 0 <>x <>oo, zero elsewhere.

(a) Show that the m.g.f. M( t; n) of Yn = Jr,( in - I ) is equal to [e'1.J,, - (t/ Jr,)e1IJnJ -n, t Jn.

(b) Find the limiting distribution of Yn as n -+ oo.

This exercise and the immediately preceding one are special instances of an important theorem that will be proved in the next section.

Reference no: EM13993193

Questions Cloud

Compute approximately the probability : Let /(x) = 1/r, 1 x oo, zero elsewhere, be the p.d.f. of a random variable X. Consider a random sample of size 72 from the distribution having this p.d.f. Compute approximately the probability that more than 50 of the observa..

Determine the directions of the currents in each resistor : Consider the circuit shown in (Figure 1) . The batteries have emfs of E1=9.0V and E2=12.0V and the resistors have values of R1=28Ω, R2=64A?©, and R3=32Ω. Determine the magnitudes of the currents in each resistor shown in the figure. Ignore interna..

Define and give examples of three strategies : Define and give examples of three strategies that are rooted in instruction design theory referred to in our Course Content: Organizational strategies. Delivery strategies. Management strategies.

Denote the mean of a random sample of size : 1. Let X denote the mean of a random sample of size 100 from a distri bution that is x2(50). Compute an approximate value of Pr (49 X 51).

Instances of an important theorem : Find the limiting distribution of Yn as n -+ oo. This exercise and the immediately preceding one are special instances of an important theorem that will be proved in the next section.

Create an initial post in which you analyse an act : Create an initial post in which you analyse an act within your country with the purpose of protecting data. Focus on how your selected act protects data.

Calculate the currents in each resistor : Calculate the currents in each resistor of the figure. Calculate the current in 25Ω resistor. Calculate the current in 120Ω resistor.

Does it appear that the realty business can pay it is debts : Identify the personal items given in the proceeding facts that would not be reported on the balance sheet of the business.

Create at least six screens representing various states : Make the purpose small and achievable. For example, imagine an application that constantly keeps you updated on what is happening in the class, with classmates posting and commenting on your work and assignments. Be sure to explain the purpose of ..

User Account

All Pages