Question: Let X and Y have joint probability density function fX,Y (x; y) = Cy exp[-xy]1 {x>1;y>1} where C > 0 is an appropriate constant. a,

Let X and Y have joint probability density function fX,Y (x; y) = Cy exp[-xy]1 {x>1;y>1} where C > 0 is an appropriate constant.

a, Evaluate C, and then find the marginal probability density functions of X and Y .

b, Find the conditional probability density function of X given

that Y = y, where y in the range of (1;inf). Are X and Y independent?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Th e ratio of defected switches in the production of these lines is 0.03 , 0.04, 0.01, 0.02 and 0.01 respectively, and required the following: a We draw a transistor of the total production of the...

Q:

EE 351K Probability, Statistics and Stochastic Processes - Spring 2016 Homework 5 Topics: Discrete and Continuous RVs Homework and Exam Grading \"Philosophy\" Answering a question is not just about...

Q:

7. On the basis of a physical examination and symptoms, a physician assesses the probabilities that the patient has no tumour, a benign tumour, or a malignant tumour as 0.70, 0.20, and 0.10,...

Q:

can someone help here please 7. For the following problems, write out the integral() that would be needed to obtain the answer. Do not calculate the integrals. The purpose of this problem is to...

Q:

. Suppose we roll a die 1000 times. What is the probability that the sum of the numbers obtained lies between 3000 and 4000? 2. Suppose Kathy flip a coin 1000 times. What is the probability she will...

Q:

Suppose X has a normal distribution with mean 0 and variance 1, Y has a chi-square distribution with n degrees of freedom, W has a chi-square distribution with p degrees of freedom, and W, X, and Y...

Q:

26. Let f (x, y) be the joint probability density function of two continuous random variables; f is called circularly symmetrical if it is a function of G x2 + y2, the distance of (x, y) from the...

Q:

4. Let X and Y have the joint density function. f(x, y) = Se-(x+y), x>0, y> 0 0, elsewhere (a) Show that this is a probability density function. (b) What is the probability that X > 1 and Y

Q:

Consider a renewal process N(t) where T1, T2, . . . are i.i.d. and uniformly distributed on [0, 1]. Derive the renewal function m(t) for t ? 1. 58 Consider a lamp where the lightbulbs are replaced...

Q:

10. (10 pints, 5+5) Let random vector (X, Y ) have the following joint probability density function f (x, y) = 10* +cy if0 0, y > 0; 0 otherwise. (1). Determine the constant c. (2). Are random...

Q:

How far from the bottom of the chute does the ball land? Your answer for the distance the ball travels from the end of the chute should contain R.

Q:

Steve Jobs and his friend Steve Wozniak were self-taught engineers who created one of the most popular, revolutionary, technology brand, Apple. Steve Jobs was not the first person to have an idea to...

Q:

annully and are currently priced to provide a yield of 1 4 k . What is the grice must a new investor pay to purchase the bonds? 4 7 3 9 . 1 7 $ 1 , 3 2 0 : 8 3 8 1 , 1 9 8 . 8 2 1 7 3 5 . 1 5 None of...

Q:

An art professor wants to create a visual word display. The art professor chooses the word "byte" and says that each letter of the words "byte" must have a certain height and a certain width. Also...