Call Now to Set Up Tutoring:

(757) 689-7080

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Probability Theory Resources

3 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Probability Theory but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Probability Theory flashcards! Our Probability Theory flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Probability Theory flashcards.

Flashcards: Conditional Distributions and Independence

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

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 2 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

c = 6

c = 2

c = 1

c = 12

$c = \frac{3}{2}$

Report an Error Copyright Notice

Flashcards: Conditional Distributions and Independence

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

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 2 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Your answer:

c = 2

Your answer:

c = 1

Your answer:

c = 12

Your answer:

$c = \frac{3}{2}$

Correct answer:

c = 6

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

$\int_{0}^{\infty}\int_{0}^{y} c e^{- x - 2 y}\, dx\, dy$

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.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- x - 2 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} c e^{- 2 y} - c e^{- 3 y}\, dy = 1$

To evaluate this, we need to use the limit definition

$\lim_{b \to \infty}\left(- \frac{c}{2} e^{- 2 y} + \frac{c}{3} e^{- 3 y}\right) \Big|_{ 0 }^{ b }$

$- \lim_{b \to \infty}\left(- \frac{c}{6}\right) + \lim_{b \to \infty}\left(- \frac{c}{2} e^{- 2 b} + \frac{c}{3} e^{- 3 b}\right)$

$\frac{c}{6} = 1$

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

c = 6

Flashcards: Conditional Distributions and Independence

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

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 19 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

$c = \frac{1}{400}$

$c = \frac{1}{380}$

c = 380

c = 400

c = 360

Report an Error Copyright Notice

Flashcards: Conditional Distributions and Independence

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

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 19 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Your answer:

$c = \frac{1}{400}$

Your answer:

$c = \frac{1}{380}$

Your answer:

c = 400

Your answer:

c = 360

Correct answer:

c = 380

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.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- x - 19 y}\, dx\, dy$

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.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- x - 19 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} c e^{- 19 y} - c e^{- 20 y}\, dy = 1$
To evaluate this, we need to use the limit definition

$\lim_{b\to \infty}\left(- \frac{c}{19} e^{- 19 y} + \frac{c}{20} e^{- 20 y}\right) \Big|_{ 0 }^{ 19 }$

$- \lim_{b \to \infty}\left(- \frac{c}{380}\right) + \lim_{b\to \infty}\left(- \frac{c}{19 e^{361}} + \frac{c}{20 e^{380}}\right)$

$\frac{c}{380} = 1$

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

c = 380

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)

View Tutors

Ronald
Certified Tutor

Towson University, Master of Science, Counseling Psychology.

View Tutors

Catherine
Certified Tutor

Chowan University, Bachelor of Science, Psychology.

View Tutors

Jillian
Certified Tutor

Virginia State University, Bachelor of Science, Multi-/Interdisciplinary Studies, General.

Popular Subjects

SAT Tutors in Houston, Math Tutors in Los Angeles, Algebra Tutors in San Diego, Math Tutors in Houston, GRE Tutors in Phoenix, Biology Tutors in Seattle, French Tutors in Denver, GRE Tutors in Denver, GMAT Tutors in San Diego, MCAT Tutors in Phoenix

Popular Courses & Classes

LSAT Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in Boston, SAT Courses & Classes in San Diego, SAT Courses & Classes in Chicago, ACT Courses & Classes in New York City, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC

Popular Test Prep

GMAT Test Prep in San Diego, SAT Test Prep in Boston, GRE Test Prep in Phoenix, SAT Test Prep in Atlanta, GMAT Test Prep in Los Angeles, ACT Test Prep in New York City, SSAT Test Prep in Washington DC, SSAT Test Prep in Philadelphia, SAT Test Prep in Philadelphia, SAT Test Prep in Washington DC

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Probability Theory Resources

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All Probability Theory Resources

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Flashcards: Conditional Distributions and Independence

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: