Call Now to Set Up Tutoring:

(888) 888-0446

Probability Theory : Probability Theory

Study concepts, example questions & explanations for Probability Theory

Create An Account

All Probability Theory Resources

3 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Probability Theory

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 10 x - 10 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Possible Answers:

$c = \frac{200}{3}$

c = 1

c = 400

c = 200

c = 50

Correct answer:

c = 200

Explanation:

In order to find the value of $\uptext{c}$ , we need to take find the double integral of the function

Let's find what the bounds are for both $\uptext{x}$ , and $\uptext{y}$

We look at the p.d.f to see that the bounds for $\uptext{x}$ are, 0<x<y , and for $\uptext{y}$ , $0<y<\infty$

Now let's set up the double integral

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 10 x - 10 y}\, dx\, dy$

Before we evaluate it, we need to remember to set the double integral equal to one, since we are essentially solving for the c.d.f.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 10 x - 10 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} \frac{c}{10} e^{- 10 y} - \frac{c}{10} e^{- 20 y}\, dy = 1$

To evaluate this, we need to use the limit definition

$\lim_{b \to \infty}\left(- \frac{c}{100} e^{- 10 y} + \frac{c}{200} e^{- 20 y}\right) \Big|_{ 0 }^{ b }$

$- \lim_{b \to \infty}\left(- \frac{c}{200}\right) + \lim_{b \to \infty}\left(- \frac{c}{100} e^{- 10 b} + \frac{c}{200} e^{- 20 b}\right)$

$\frac{c}{200} = 1$

Now we simply solve for $\uptext{c}$

c = 200

Report an Error

Example Question #12 : Probability Theory

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 9 x - 11 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Possible Answers:

c = 440

c = 220

$c = \frac{220}{3}$

c = 55

c = 1

Correct answer:

c = 220

Explanation:

Before we evaluate it, we need to remember to set the double integral equal to one, since we are essentially solving for the c.d.f.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 9 x - 11 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} \frac{c}{9} e^{- 11 y} - \frac{c}{9} e^{- 20 y}\, dy = 1$

To evaluate this, we need to use the limit definition

$\lim_{b \to \infty}\left(- \frac{c}{99} e^{- 11 y} + \frac{c}{180} e^{- 20 y}\right) \Big|_{ 0 }^{ b }$

$- \lim_{b \to \infty}\left(- \frac{c}{220}\right) + \lim_{b \to \infty}\left(- \frac{c}{99} e^{- 11 b} + \frac{c}{180} e^{- 20 b}\right)$

$\frac{c}{220} = 1$

Now we simply solve for $\uptext{c}$

c = 220

Report an Error

View Tutors

Mark
Certified Tutor

Murray State University, Bachelor of Science, Mathematics.

View Tutors

Alex
Certified Tutor

Vanderbilt University, Bachelor of Science, Psychology. Boston University, Master of Science, Speech-Language Pathology.

View Tutors

Wura
Certified Tutor

CUNY Bernard M Baruch College, Bachelor in Arts, Business Communications. McDaniel College, Master of Science, Teaching Engli...

All Probability Theory Resources

3 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Miami, Spanish Tutors in San Francisco-Bay Area, Computer Science Tutors in Dallas Fort Worth, SSAT Tutors in San Francisco-Bay Area, GMAT Tutors in Denver, MCAT Tutors in Philadelphia, Math Tutors in Atlanta, Algebra Tutors in Chicago, Computer Science Tutors in Atlanta, Calculus Tutors in San Francisco-Bay Area

Popular Courses & Classes

ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in New York City, ACT Courses & Classes in Seattle, GRE Courses & Classes in Washington DC, SAT Courses & Classes in Washington DC, GMAT Courses & Classes in Houston, GMAT Courses & Classes in Seattle, GMAT Courses & Classes in Miami, ACT Courses & Classes in Phoenix, SSAT Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in Chicago, MCAT Test Prep in Philadelphia, GMAT Test Prep in Chicago, GMAT Test Prep in Denver, SAT Test Prep in Philadelphia, MCAT Test Prep in San Diego, SSAT Test Prep in Atlanta, ISEE Test Prep in Los Angeles, MCAT Test Prep in Boston, GRE Test Prep in Philadelphia

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Probability Theory : Probability Theory

Study concepts, example questions & explanations for Probability Theory

All Probability Theory Resources

Example Questions

Example Question #11 : Probability Theory

Example Question #12 : Probability Theory

All Probability Theory Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: