/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 5.14 Let X聽be a uniform (0,1)聽rando... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.14 (page 213)

Let Xbe a uniform (0,1)random variable. Compute role="math" localid="1646717640777" EXnby using Proposition 2.1, and then check the result by using the definition of expectation.

Short Answer

Expert verified

The required answer isEXn=1n+1.

Step by step solution

01

Step 1. Given Information.

Here, it is given that: Xis a uniform0,1random variable.

02

Step 2. Write the probability density function of uniform distribution.

Let Xbe a random variable and follows a uniform distribution with parameters a=0andb=1.

The probability density function of uniform distribution is f(x)=1b-a;a<x<b

03

Step 3. Calculate EX from the expectation definition for uniform distribution Ua,b.

EX=鈭�abx1b-adx=鈭�01x11-0dx=鈭�01xdx

04

Step 4. Compute EXn by using definition of expectation.

EXn=鈭�01xdx=xn+1n+101=1n+1n+1-0n+1n+!=1n+1鈭�EXn=1n+1

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let X be a normal random variable with mean 12and variance 4. Find the value of csuch that localid="1646649699736" PX>c=0.10.

The lifetimes of interactive computer chips produced

by a certain semiconductor manufacturer are normally distributed with parameters渭=1.4脳106hours and 蟽=3脳105hours. What is the approximate probability that abatch of 100chips will contain at least 20whose lifetimes are less than 1.8脳106?

Suppose that X is a normal random variable with

mean 5. If P{X > 9} = .2, approximately what is Var(X)?

Find the probability density function of Y = eX when X is normally distributed with parameters 渭 and 蟽2. The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with parameters 渭 and 蟽2.

A standard Cauchy random variable has density function

f(x)=1蟺1+x2鈭�鈭�<x<鈭�

Show that if X is a standard Cauchy random variable, then 1/X is also a standard Cauchy random variable.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.