Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q 5.38 (page 214)

If Yis uniformly distributed over (0,5),what is the probability that the roots of the equation 4x2+4xY+Y+2=0are both real?

Short Answer

Expert verified

Thus, the probability of real roots isP{Y≥2}=35

Step by step solution

01

Given information:

Yis uniformly distributed on(0,5)

02

Explanation:

The two roots of the quadratic are:

x=-416Y2-16(Y+2)8=12-1±Y2-Y-2

The roots are real if and only ifY2-Y-2≥0.consider next the roots of the equationy2-y-2=0. Then solution isy=1±1+82=1±32=-1or2

03

EXPLANATION:

This means thaty2-y-2=(y+1)(y-2)which can be checked directly too. Consequently,Y2-Y-2≥0if and only ifY-2≥0. Thus, the probability of real roots isP{Y≥2}=35

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by

f(x)=10x2x>100x≤10

(a)FindP{X>20}

localid="1646589462481" (b)What is the cumulative distribution function of localid="1646589521172" X?

localid="1646589534997" (c)) What is the probability that of6such types of devices, at least localid="1646589580632" 3will function for at least localid="1646589593287" 15hours? What assumptions are you making?

Evidence concerning the guilt or innocence of a defendant in a criminal investigation can be summarized by the value of an exponential random variable X whose mean μ depends on whether the defendant is guilty. If innocent, μ = 1; if guilty, μ = 2. The deciding judge will rule the defendant guilty if X > c for some suitably chosen value of c.

(a) If the judge wants to be 95 percent certain that an innocent man will not be convicted, what should be the value of c?

(b) Using the value of c found in part (a), what is the probability that a guilty defendant will be convicted?

A standard Cauchy random variable has density function

f(x)=1π1+x2−∞<x<∞

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

If 65percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability that a random sample of 100people will contain

(a) at least 50who are in favor of the proposition;

(b) between 60and 70inclusive who are in favor;

(c) fewer than 75in favor.

The lung cancer hazard rateλ(t)of a t-year-old male smoker is such that

λ(t)=.027+.00025(t−40)2t≥40

Assuming that a 40-year-old male smoker survives all other hazards, what is the probability that he survives to

(a)age50and (b)age 60 without contracting lung cancer?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure 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.

Sign-up for free