Question: The joint probability density function of the random variables X, Y , and Z is Find (a) the joint marginal density function of Y and

The joint probability density function of the random variables X, Y , and Z is

4ryz? 4ryz, 0< x, y < 1, 0< z < 3, f(x, y, z) = elsewhere. 0,


Find
(a) the joint marginal density function of Y and Z;
(b) the marginal density of Y;
(c) P( < X < }, Y >, 1 < Z < 2);

(d)4ryz? 4ryz, 0 < x, y < 1, 0 < z <

4ryz? 4ryz, 0 < x, y < 1, 0 < z < 3, f(x, y, z) = elsewhere. 0, P( < X < }, Y >, 1 < Z < 2);

Step by Step Solution

★★★★★

3.40 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b c d Sin... 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 Essentials of Statistics Questions!

Q:

The joint probability density function of the random variables X, Y, and Z is find (a) The joint marginal density functions of Y and Z: (b) The marginal density of Y; (c) P (1/4 , KZ

Q:

Consider the following joint probability density function of the random variables X and Y: (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).

Q:

Joint probability distributions of three or more random variables can be interpreted by extending the ideas in this section. I-'or example, suppose that three continuous random variables X, Y, and Z...

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:

3. Let p(x, y, z) = (xyz)/162, x = 4, 5, y = 1, 2, 3, and z = 1, 2, be the joint probability mass function of the random variables X, Y , Z. (a) Calculate the joint marginal probability mass...

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:

12. For = (x, y) : 0 , a region in the plane, let be the joint probability density function of the random variables X and Y . Find the marginal probability density functions of X and Y, and P(X + Y >...

Q:

4. If the joint probability density function of the random variables X and Y is given by f(I, y) = 1 0 k(r' ty) for (x, y) ED elsewhere where D is the region enclosed by r-axis, y-axis and a ty = 1....

Q:

Consider the following joint probability density function of the random variables X and Y : f(x, y) = 3xy 9 , 1

Q:

3.68 Consider the following joint probability density function of the random variables X and Y : f(x, y) = 3x y 11 , 1

Q:

A uniform 75-kg cube is attached to a uniform 70-kg circular shaft as shown and a couple M of constant magnitude 20 N ?? m is applied to the shaft. Knowing that r = 100 mm and L = 300 mm, determine...

Q:

Vozniak Company began business on January 1, 20-1. Purchases and sales during the month of January follow. REQUIRED Calculate the total amount to be assigned to cost of goods sold for January and the...

Q:

The asset and capital plans ascertain whether the enterprise has resources sufficient to realize the firm's revenue objectives. True or false.

Q:

Using Appendix Data Set or the file on the web named ADD.dat, a. What is the probability that a male will have an ADDSC score greater than 50 if the scores are normally distributed with a mean of...

Q:

What is the difference between parametric tests and non-parametric tests?

Q:

For each of the following examples, identify whether the research has expressed a directional or a nondirectional hypothesis: a. A researcher is interested in studying the relation between the use of...

Q:

For each of the following examples (the same as those in Exercise 7.41), state the null hypothesis and the research hypothesis, in both words and symbolic notation: a. A researcher is interested in...

Q:

( get the stock price of any five companys for diffrent firms but it important that are from previous month then cluculate its for Investment and protoflio course ) ( get the stock price of any five...

Q:

The next dividend payment by Hoffman, Inc., will be $2.55 per share. The dividends are anticipated to maintain a growth rate of 6 percent forever. Assume the stock currently sells for $48.70 per...

Q:

You want to buy a new sports car 3 years from now, and you plan to save $ 6 , 2 0 0 per year, beginning one year from today. You will deposit your savings in an account that pays 5 . 2 % interest....