Question: Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3).

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3).
a. For 0 < y < 3, find the conditional density fX|Y (x | y) of X, given Y = y.
b. Find the conditional probability that X ≤ 1, given Y = 1.
c. Find the conditional probability that X ≤ 1, given Y ≤ 1.

Step by Step Solution

★★★★★

3.45 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The joint density is 2 9 because the ar... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

760-M-S-P (6352).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Consider a pair of random variables X, Y with joint density fX,Y(x, y) = 8e-2x-4y, for 0

For positive constants and, a pair of random variables has a joint PDF specified by . Fx, y (x, y) = abe-(ax = by) u (x) u (y) (a) Find the joint CDF, Fx, y (x, y). (b) Find the marginal PDFs, fx (x)...

A pair of random variables has a joint PDF specified by (a) Find (X > 2, Y (b) Find Pr (0 2. (c) Find Hint: Set up the appropriate double integral and then use the change of variables: u = x y, v =...

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3). a. Find the expected value of the sum of X and Y, i.e., find E(X +...

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3). Find P (X + Y > 2).

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3). Find the expected value E(X). (by symmetry, E(Y) is just the same!)

14. Consider a pair of random variables X; Y with constant joint density on the quadrilateral with vertices (0; 0), (2; 0), (2; 6), (0; 12). a) Find the variance of X, i.e., find Var(X). b) Find the...

Consider a pair of random variables X, Y with constant joint density on the quadrilateral with vertices (0, 0), (2, 0), (2, 6), (0, 12). a. Find the variance of X, i.e., find Var X. b. Find the...

Consider a pair of random variables X, Y with constant joint density on the quadrilateral with vertices (0, 0), (2, 0), (2, 6), (0, 12). a. Find the expected value E(X). b. Find the expected value...

Consider a pair of random variables X, Y with constant joint density on the quadrilateral with vertices (0, 0), (2, 0), (2, 6), (0, 12). Find P (Y 3X).

What ethical rules can help managers to best allocate authority and design their hierarchies?

Forbes lists Bill Gates and Warren Buffet as the two wealthiest Americans. Do these two men face scarcity?

2 0 Multiple Choice 1 point You are using internal rate of return ( IRR ) to evaluate several alternative investments for your client, Jerry. If Jerry's required rate of return is 8 % , which of the...

What is included in the project schedule? a) Project budget b) Detailed project timeline with start and finish dates for each activity c) Stakeholder register d) Risk management plan

Many opinion polls have tracked opinions regarding the fear of terrorist attacks following the September 11, 2001, attacks on the World Trade Center. A Newsweek poll conducted by Princeton Survey...

The mobile Internet is growing, with users accessing sites such as Yahoo! Mail, the Weather Channel, ESPN, Google, Hotmail, and Mapquest from their cell phones. The most popular web browsers are...

An advertisement in a recent Time magazine claimed that Geico Insurance will help you save an average of $200 per year on your automobile insurance. 15 a. Construct a relative frequency histogram to...

File Processing Complete the class code below and write a static method named reverseLines that accepts a Scanner containing an input file as a parameter and that echoes the input file to System.out...

The treasurer of a large corporation wants to invest $33 million in excess short-term cash in a particular money market investment. The prospectus quotes the instrument at a true yield of 4.21...

Setrakian Industries needs to raise $67.2 million to fund a new project. The company will sell bonds that have a coupon rate of 5.74 percent paid semiannually and that mature in 15 years. The bonds...