Call Now to Set Up Tutoring:

(888) 888-0446

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: 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.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 2 x - 10 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

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

c = 240

c = 30

c = 120

c = 40

c = 1

Report an Error Copyright Notice

Flashcards: 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.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 2 x - 10 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

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

Your answer:

c = 240

Your answer:

c = 30

Your answer:

c = 40

Your answer:

c = 1

Correct answer:

c = 120

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

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 2 x - 10 y}\, dx\, dy$

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.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 2 x - 10 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} \frac{c}{2} e^{- 10 y} - \frac{c}{2} e^{- 12 y}\, dy = 1$

To evaluate this, we need to use the limit definition

$\lim_{b \to \infty}\left(- \frac{c}{20} e^{- 10 y} + \frac{c}{24} e^{- 12 y}\right) \Big|_{ 0 }^{ b }$

$- \lim_{b \to \infty}\left(- \frac{c}{120}\right) + \lim_{b \to \infty}\left(- \frac{c}{20} e^{- 10 b} + \frac{c}{24} e^{- 12 b}\right)$

$\frac{c}{120} = 1$

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

c = 120

Flashcards: 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.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 6 x - 10 y} & 0<x<y<\infty \\ 0, & \text{Otherwise} \end{cases}$

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

c = 1

c = 320

c = 160

c = 40

$c = \frac{160}{3}$

Report an Error Copyright Notice

Flashcards: Probability Theory

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

Your answer:

c = 1

Your answer:

c = 320

Your answer:

c = 40

Your answer:

$c = \frac{160}{3}$

Correct answer:

c = 160

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

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 6 x - 10 y}\, dx\, dy$

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.

$\int_{0}^{\infty}\int_{0}^{y} c e^{- 6 x - 10 y}\, dx\, dy = 1$

Now evaluate the double integral

$\int_{0}^{\infty} \frac{c}{6} e^{- 10 y} - \frac{c}{6} e^{- 16 y}\, dy = 1$

To evaluate this, we need to use the limit definition

$\lim_{b \to \infty}\left(- \frac{c}{60} e^{- 10 y} + \frac{c}{96} e^{- 16 y}\right) \Big|_{ 0 }^{ b }$

$- \lim_{b \to \infty}\left(- \frac{c}{160}\right) + \lim_{b \to \infty}\left(- \frac{c}{60} e^{- 10 b} + \frac{c}{96} e^{- 16 b}\right)$

$\frac{c}{160} = 1$

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

c = 160

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

Matt
Certified Tutor

View Tutors

Francisco
Certified Tutor

The University of Texas at El Paso, Bachelor of Science, Physics.

View Tutors

Danielle
Certified Tutor

Florida State University, Bachelors, English. Florida State University, Current Grad Student, History.

Popular Subjects

Statistics Tutors in Seattle, Algebra Tutors in Houston, Algebra Tutors in Dallas Fort Worth, Reading Tutors in Washington DC, Calculus Tutors in Washington DC, Spanish Tutors in Chicago, GMAT Tutors in Dallas Fort Worth, ISEE Tutors in Los Angeles, ISEE Tutors in Dallas Fort Worth, Math Tutors in Seattle

Popular Courses & Classes

LSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Boston, ACT Courses & Classes in Philadelphia, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Houston, LSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Phoenix, LSAT Courses & Classes in New York City, MCAT Courses & Classes in Seattle, MCAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Washington DC, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Houston, GRE Test Prep in Atlanta, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in New York City, SAT Test Prep in Phoenix, ISEE Test Prep in Chicago, SSAT Test Prep in San Diego, MCAT Test Prep in Los Angeles

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: Probability Theory

Flashcards: Probability Theory

Flashcards: Probability Theory

Flashcards: Probability Theory

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: Probability Theory

Flashcards: Probability Theory

Flashcards: Probability Theory

Flashcards: Probability Theory

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: