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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2 - Problem 20se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2 - Problem 20se

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# Refer to Exercise 19.a. Find ?X.________________b. Find

ISBN: 9780073401331 38

## Solution for problem 20SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Problem 20SE

Problem 20SE

Refer to Exercise 19.

a. Find μX.

b. Find μY.

c. Find σX.

d. Find σY.

e. Find Cov(X, Y).

f. Find ρX,Y.

Step-by-Step Solution:
Step 1 of 3

Step1 of 7:

From exercise 19.

The joint probability mass function of tensile strength (y) and additive concentration (x).

 Tensile strength (y) Concentration of additive (x) 100 150 200 0.02 0.05 0.06 0.11 0.22 0.04 0.01 0.08 0.10 0.19 0.06 0.04 0.08 0.17 0.29 0.08 0.04 0.14 0.12 0.3 0.14 0.36 0.5

Step2 of 7:

a). We need to find .

That is,

= 0.02(0.22) + 0.04(0.19) + 0.06(0.29) + 0.08(0.3)

= 0.0534.

Therefore, = 0.0534.

Step3 of 7:

b). To find

That is,

= 100(0.14) + 150(0.36) + 200(0.5)

= 168.

Therefore, = 168.

Step4 of 7:

c). To find

That is,

=(0.22) +

= 0.00050444

= 0.02246.

Therefore, = 0.02246.

Step5 of 7:

d). To find

That is,

= 1276.

= 35.7211

Therefore, = 35.7211

Step6 of 7:

e). To find Cov(X,Y).

Then,

Now,

=

+

(0.08)(100)P(0.08 and 100) + (0.08)(150)P(0.08 and 150) + (0.08)(200)P(0.08 and 200).

+

(0.08)(100)(0.04) + (0.08)(150)(0.14) + (0.08)(200)(0.12).

= 8.96.

Therefore,

= 8.96 - (0.0534)(168)

= 8.96 - 8.9712

= - 0.0112.

Therefore,

Step7 of 7:

f). To find

=

= -0.01396

Therefore,

Step 2 of 3

Step 3 of 3

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