/*! 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.4.6 Let X聽be such that聽P{X=1}=p=1-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q.4.6 (page 170)

Let Xbe such thatP{X=1}=p=1-P{X=-1}

Find c鈮�1such that EcX=1.

Short Answer

Expert verified

The two possible values of c are p and 1p-1.

Step by step solution

01

Given information

Given in the question that,

P{X=1}=p=1-P{X=-1}.

02

Calculation

Observe that random variable Xassumes only two values with positive probability. We have that

P(X=1)=p

P(X=-1)=1-p

Using the theorem about the expectation of a function of a random variable,

We have that

1=EcX=c脳p+1c(1-p)

Multiply both sides with c, we end up with an equation

pc2-c+(1-p)=0.

03

Solution

Two solutions are,

c1,2=1卤1-4p(1-p)2p

Observe that the term under the root is equal to (2p-1)2, so we have

c1,2=1卤|2p-1|2p

Therefore, we get that we have two answers

c1=1,c2=1-pp.

04

Final answer

There exist two possible values of c. They are p and 1p-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

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10times and the man is asked to predict the outcome in advance. He gets 7out of 10 correct. What is the probability that he would have done at least this well if he did not have ESP?

An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2 3 , what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of

(a) 5 people and

(b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly

(c) 6 people and

(d) 7 people on the list?

Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always bets that the outcome will be one of the numbers 1 through 12, what is the probability that

  1. Smith will lose his first 5 bets;
  2. his first win will occur on his fourth bet?

A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.

If you buy a lottery ticket in 50lotteries, in each of which your chance of winning a prize is role="math" localid="1646465220038" 1100, what is the (approximate) probability that you will win a prize

(a) at least once?

(b) exactly once?

(c) at least twice?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.