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# Let a, b, c, d be any numbers with a<b and c<d. Let k be a ISBN: 9780073401331 38

## Solution for problem 33E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 33E

Let a, b, c, d be any numbers with a<b and c<d. Let k be a constant, and let X and Y be jointly continuous with joint probability density function In other words, f(x, y) is constant on the rectangle a<x<b and c<y<d, and zero off the rectangle.

a. Show that b. Show that the marginal density of X is fX(x) = 1/(b - a) for a<x<b.

c. Show that the marginal density of Y is fY(y) = 1/(d - c) for c<y<d.

d. Use parts (a), (b); and (c) to show that X and Y are independent.

Step-by-Step Solution:

Step 1 of 5</p>

Here given the joint probability function with constant K

From that we need to find the value of k

Marginal probabilities functions of X and Y

And we have to show that X and Y independent

The given function is =0 , otherwise

Step 2 of 5</p>

a) We know that total probability is one     Step 3 of 5</p>

b) the marginal density function of X is = = =1/(b-a)

Hence 1/(b-a) for a<x<b

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

The answer to “Let a, b, c, d be any numbers with a<b and c<d. Let k be a constant, and let X and Y be jointly continuous with joint probability density function In other words, f(x, y) is constant on the rectangle a<x<b and c<y<d, and zero off the rectangle.a. Show that ________________b. Show that the marginal density of X is fX(x) = 1/(b - a) for a<x<b.________________c. Show that the marginal density of Y is fY(y) = 1/(d - c) for c<y<d.________________d. Use parts (a), (b); and (c) to show that X and Y are independent.” is broken down into a number of easy to follow steps, and 95 words. The full step-by-step solution to problem: 33E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 33E from 2.6 chapter was answered, more than 267 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: show, let, Density, constant, rectangle. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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