Question: The joint density function of two random variables (X) and (Y) is given by [p_{X, Y}(x, y)= begin{cases}frac{x y}{9}, & 0 leq x leq 2,0

The joint density function of two random variables \(X\) and \(Y\) is given by

\[p_{X, Y}(x, y)= \begin{cases}\frac{x y}{9}, & 0 \leq x \leq 2,0 \leq y \leq 3 \\ 0, & \text { elsewhere }\end{cases}\]

(a) Find the marginal density functions of \(X\) and \(Y\).

(b) Find the means and standard deviations of \(X\) and \(Y\).

(c) Find the correlation coefficient \(ho_{X, Y}\).

Step by Step Solution

★★★★★

3.36 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To find the marginal density functions of X and Y we integrate the joint density function over the ... View full answer

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 Mechanical Vibration Analysis Questions!

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

Write an alternative definition that is tail-recursive (iterative) and makes use of accumulator variables. [10 marks] Explain why your alternative definition executes more efficiently. [3 marks] 1...

Q:

Which of the following group of accounts are increased with a debit? a. assets, liabilities, owner's equity b. assets, drawing, expenses c. assets, revenues, expenses d. assets, liabilities, revenues

Q:

Probability and statistics Problem #5 Let X denote the 'transpiration' (ml/h) and Y denote the corresponding ammonium concentration(mg/L) 5 points Data collected from an experiment is given as...

Q:

5.11 The joint probability density function of two random variables X and X is given by fx1, x(x1, x2) = { = K, 0. 1 0, 2 0, x1 + x2 2 otherwise. (a) Find the value of K that makes fx,x(x1, x2) a...

Q:

The joint probability density function of two random variables (X and Y) is given by fX,Y (x, y) = ( C y (y ^(+1)) exp {( y(2+x ^2 ) )/2 } , x (,), y [0,), 0 otherwise. (a) Find C. (b) Find the...

Q:

6. Let the joint probability density function of two random variables X and Y be given by Find E(X | Y = y), E(Y | X = x), and (X, Y ). Hint: To find , use Lemma 10.3. 2 if 0

Q:

solve please 7. Suppose that the joint probability density function of two random variables X and Y is Ax, y) = c(xty) for x between 0 and 2, and for y between 0 and 1, and zero off of this...

Q:

2. Consider the following joint probability density function of two random variables X and Y: 1 0.20 0.30 0.06 X 0 0.27 0.10 0.07 fy (y) 0 Y 1 2 fx(x) where fy (y) is the marginal probability density...

Q:

both questions Suppose the joint density of two continuous random variables X and Y is given by f(x; y) = ( 1 6 (x2y + xy2) if 0 x 1; 0 y 3 0 elsewhere : (a) Find the conditional density of X given Y...

Q:

Explain how a person can use a cybersignature and why the subject of cybersignatures is significant.

Q:

A three-phase induction motor, operating at rated voltage and frequency, has a starting torque of 135 percent and a maximum torque of 220 percent, both with respect to its rated-load torque....

Q:

Suppose the United States and India were the only two countries in the world. a. Draw a correctly labeled graph of the foreign exchange market for U.S. dollars showing the equilibrium in the market....

Q:

Using the following information about a single product com pany, compute its total actual cost of direct materials used. Direct materials standard cost: 5 lbs. X $2 per lb. = $10. Total direct...

Q:

Repeat Problem 39 using MATLAB. The program will do the following in one program: a. Display a root locus and pause. b. Display a close-up of the root locus where the axes go from -2 to 0.5 on the...

Q:

Sketch the root locus for the system of Figure P8.12 and find the following: a. The range of gain to yield stability b. The value of gain that will yield a damping ratio of 0.707 for the systems...

Q:

For the system shown in Figure P8.11, do the following: a. Sketch the root locus. b. Find the j-axis crossing and the gain, K, at the crossing. c. Find the real-axis breakaway to two-decimal-place...

Q:

Consider the following information: State of Economy Probability of State of Economy Portfolio Return If State Occurs Recession .22 .12 Boom .78 .22 Calculate the expected return. (Do not round...

Q:

On October 2, 2020, Crane Company sold $6,520 of its elite camping gear (with a cost of $3,240 ) to Lynch Outfitters. As part of the sales agreement, Crane includes a provision that if Lynch is...

Q:

1. Omar Inc, manufactures an advanced swim fin for seuba divers. Management is now prepuring denaled bodgets for the third quarter, July through September, and has assembled the following information...