Deduce that the random variable

Assignment Help Basic Statistics
Reference no: EM13688002

a) If X1...Xn are independent U(0,1) random variables and Y = ( ∏ from i=1 to n of Xi)^1/n, show that nlogY has m.g.f. (1 + z)^-n. i=1 (Hint: first find the m.g.f. of log Xi. 

(b) Suppose that Y has density [n^n/(n-1)!](-y log y)^n-1 on (0,1). Show that E(Y^nz) =(1 + z)^-n. (Hint: start by substituting t = -log y.) (Here you may use the fact that integral form 0 to infinity of (s^n-1)ds = (n-1)! for n = 1, 2...) 

 

(c) Deduce that the random variable Y in (a) has the density given in (b).

Reference no: EM13688002

Questions Cloud

Discover the government budget deficit or surplus : Discover the government budget deficit or surplus. Compute the Equilibrium level (Y) Compute the equilibrium level of disposable Income (Yd). Compute the level of Consumption (C) in equilibrium.
Consumption function-what is the multiplier in this economy : Normal 0 false false false EN-US X-NONE X-NONE The consumption function is ..
Statements concerning the price elasticity of demand : An increase in each of the following factors would normally provide a subsequent increase in demand, except: A price elasticity (ED) of -1.50 indicates that for a _________ increase in price, quantity demanded will __________ by ____________. Which o..
A food inspector : A food inspector, examining 12 jars of a certain brand of peanut butter, obtained from the fofollowing percentages of impurities: 2.3, 1.9, 2.1, 2.8, 2.3, 3.6, 1.4, 1.8, 2.1, 3.2, 2.0 and 1.9.
Deduce that the random variable : Deduce that the random variable Y in (a) has the density given in (b).
Based on the results shown in the following table : Based on the results shown in the following table, test at the 0.05 level of significance whether there is a relationship between parents' reaction to the course and the number of children that they have in the school system
Use the data shown in the following table to test : Use the data shown in the following table to test at the 0.05 level of significance whether they may be looked upon as values of a binomial random variable: Number of Number of cakes sold days 0 1 1 16 2 55 3 228
Assuming that the data constitute independent random samples : Assuming that the data constitute independent random samples from normal populations with equal variances, construct a 99% confidence interval for the difference between the true average heat-producing capacities of coal from the two mines.
Formulate this problem using lp : Ballplayer selection problem:- The Dubuque Sackers, a class D baseball team, face a tough four-game road trip against league rivals in Des Moines, Davenport, Omaha, and Peoria.

Reviews

Write a Review

Basic Statistics Questions & Answers

  A recent broadcast of a television show had a 15 share

a recent broadcast of a television show had a 15 share meaning that among 6000 monitored households with tv sets in use

  Find height of women using chebyshev-s theorem

Using the empirical rule, what is the approximate percentage of women between 156cm and 166cm? Using Chebyshev's Theorem, at least what percentage of women are between 149cm and 173cm?

  Based on data collected it determines that the expected

a local unemployment office keeps track of the number of new claims filed each day. based on data collected it

  A company is working on the construction of two shopping

explain why there must be a mistake in each of the following statements1. the probability that a student will get an a

  On which student score better relative to other students

A standard deviation of 12. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class?

  Quality control-binomial probability

The quality control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of 8 syringes taken from the batch. Suppose the batch contains 1% defective syringes.

  Inferential statistics to make managerial decisions

Can you provide some pros and cons of using descriptive and inferential statistics to make managerial decisions.

  How businesswomen should open boutique in neighborhood

Group of businesswomen wish to open a high fashion boutique in a vacant store but only if the average income in the area is at least $45,000. Use alpha=0.01 to test whether or not the businesswomen should open their boutique in this neighborhood.

  A system consists of three components that operate

a system consists of three components that operate independently. in order for the system to work component 1 must work

  Select a current exchange rate practice and explain the

discussion forum team as we continue to understand the power of economics in a global context evaluate the impact of

  Example of two tailed test

Provide an example of a situation from your personal or professional experience where an two-sample test of hypothesis of dependent samples would be useful in a decision-making process.

  Probability cars arrive during any given hour of operations

The mean arrival rate is 15 cars per hour. What is the probability that 20 or more cars will arrive during any given hour of operation?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd