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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 20e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 20e

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# The lifetimes, in months, of two components in a system, ISBN: 9780073401331 38

## Solution for problem 20E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 20E

Problem 20E

The lifetimes, in months, of two components in a system, denoted X and Y, have joint probability density function a. What is the probability that both components last longer than one month?

b. Find the marginal probability density functions fX(0) and fY(y).

c. Are X and Y independent? Explain.

Step-by-Step Solution:
Step 1 of 3

Solution 20E

Step1 of 4:

Let us consider a random variables X and Y they presents the lifetimes, in months, of two components in a system and they have joint probability density function. Here our goal is:

a).We need to find the probability that both components last longer than one month?

b).We need to find the marginal probability density functions c).We need to check whether X and Y independent? Explain.

Step2 of 4:

a).   First integrate above equation with respect to “y” we get Apply integration by parts we get   Apply integral substitution and let u = -2x-y

du = -1dy    ) Substitute “u” value in above equation we get    Now,

Integrate above equation with respect x we get  Apply integral by parts we get  Let us consider u = -2x-1

du = -2   Substitute “u” value in above equation we get = { }

= 0 - (- )

= Hence, = .

Step3 of 4:

b).

The marginal probability density function is given by:      Apply integral substitution and let u = -2x-y

du = -1dy    ) Substitute “u” value in above equation we get     Therefore, marginal probability density function of is given below Similarly,

The marginal probability density function is given by:    Apply integration by parts we get Let u = -2x-y

du = -2du   Substitute “u” value in above equation we get   = Therefore, marginal probability density function of is given below Step4 of 4:

c).

Consider, =   Where, = 4xy [given] = and                    [from part (b)] = [from part (b)]

Now, =   Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

The full step-by-step solution to problem: 20E 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. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “The lifetimes, in months, of two components in a system, denoted X and Y, have joint probability density function a. What is the probability that both components last longer than one month?________________b. Find the marginal probability density functions fX(0) and fY(y).________________c. Are X and Y independent? Explain.” is broken down into a number of easy to follow steps, and 47 words. Since the solution to 20E from 2.6 chapter was answered, more than 1364 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Probability, components, Density, independent, explain. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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