EBK PROBABILITY & STATISTICS FOR ENGINE
EBK PROBABILITY & STATISTICS FOR ENGINE
16th Edition
ISBN: 9780321997401
Author: AKRITAS
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
Question
Book Icon
Chapter 1.8, Problem 17E

a.

To determine

Plot the interaction plot with pH being the trace factor.

a.

Expert Solution
Check Mark

Explanation of Solution

The interaction plot with pH being the trace factor is given as follows:

EBK PROBABILITY & STATISTICS FOR ENGINE, Chapter 1.8, Problem 17E

b.

To determine

Check whether there is interaction between the factors pH and temperature.

b.

Expert Solution
Check Mark

Answer to Problem 17E

There is interaction between the factors pH and temperature.

Explanation of Solution

From the interaction plot obtained in Part (a), it is clear that the lines of pH I and pH II are not parallel to each other. Therefore, there is interaction between the factors pH and temperature.

c.

To determine

Calculate the main pH effects and the main temperature effects.

c.

Expert Solution
Check Mark

Answer to Problem 17E

The main pH effects are αI=0.125 and αII=0.125.

The temperature effects are βA=6.375,βB=0.375,βC=2.625, and βD=4.125.

Explanation of Solution

The overall mean is computed as follows:

μ¯..=108+103+101+100+111+104+100+988=103.125

The main pH effects are calculated as follows:

αI=μ¯I.μ¯..=108+103+101+1004103.125=0.125αII=μ¯II.μ..=111+104+100+984103.125=0.125

Therefore, the main pH effects are αI=0.125 and αII=0.125.

The main temperature effects are calculated as follows:

βA=μ¯A.μ¯..=108+1112103.125=6.375βB=μ¯B.μ..=103+1042103.125=0.375βC=μ¯C.μ..=101+1002103.125=2.625βD=μ¯D.μ..=100+982103.125=4.125

Therefore, the main Pygmalion effects are βA=6.375,βB=0.375,βC=2.625, and βD=4.125.

d.

To determine

Calculate the interaction effects.

d.

Expert Solution
Check Mark

Answer to Problem 17E

The interaction effects are γIA=1.375,γIB=0.375,γIC=0.625, γID=1.125,γIIA=1.375,γIIB=0.375,γIIC=0.625,and γIID=1.125.

Explanation of Solution

The interaction effects are calculated as follows:

γIA=μIA(μ¯..+αI+βA)=108(103.1250.125+6.375)=1.375γIB=μIB(μ¯..+αI+βB)=103(103.1250.125+0.375)=0.375γIC=μIC(μ¯..+αI+βC)=101(103.1250.1252.625)=0.625γID=μID(μ¯..+αI+βD)=100(103.1250.1254.125)=1.125γIIA=μIIA(μ¯..+αII+βA)=111(103.125+0.125+6.375)=1.375γIIB=μIIB(μ¯..+αII+βB)=104(103.125+0.125+0.375)=0.375γIIC=μIIC(μ¯..+αII+βC)=100(103.125+0.1252.625)=0.625γIID=μIID(μ¯..+αII+βD)=98(103.125+0.1254.125)=1.125

Therefore, the interaction effects are γIA=1.375,γIB=0.375,γIC=0.625, γID=1.125,γIIA=1.375,γIIB=0.375,γIIC=0.625,and γIID=1.125.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
QUESTION 18 - 1 POINT Jessie is playing a dice game and bets $9 on her first roll. If a 10, 7, or 4 is rolled, she wins $9. This happens with a probability of . If an 8 or 2 is rolled, she loses her $9. This has a probability of J. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on her first roll. Round to the nearest cent if necessary. Do not round until the final calculation. Provide your answer below:
5 of 5 (i) Let a discrete sample space be given by Ω = {ω1, 2, 3, 4}, Total marks 12 and let a probability measure P on be given by P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1. = Consider the random variables X1, X2 → R defined by X₁(w3) = 1, X₁(4) = 1, X₁(w₁) = 1, X₁(w2) = 2, X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2. Find the joint distribution of X1, X2. (ii) [4 Marks] Let Y, Z be random variables on a probability space (N, F, P). Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the joint distribution of Y, Z on [0,1] × [0,2] be given by 1 dPy,z(y, z) (y²z + y²²) dy dz. Find the distribution Py of the random variable Y. [8 Marks]
Total marks 16 5. Let (,,P) be a probability space and let X : → R be a random variable whose probability density function is given by f(x) = }}|x|e¯|×| for x Є R. (i) (ii) Find the characteristic function of the random variable X. [8 Marks] Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1, 2. (iii) What is the variance of X? [6 Marks] [2 Marks]
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON
Text book image
A First Course in Probability
Probability
ISBN:9780321794772
Author:Sheldon Ross
Publisher:PEARSON