Ace - AI Tutor
Ask Our Educators
Textbooks
My Library
Flashcards
Scribe - AI Notes
Notes & Exams
Download App
Naveen Ragav

Naveen R.

Divider

Viewed Questions

A textile company weaves a certain fabric on a large number of looms. The managers would like the looms to be homogeneous so that their fabric is of uniform strength. It is suspected that there may be significant variation in strength among looms. Consider the following data for 4 randomly selected looms. Each observation is a determination of strength of the fabric in pounds per square inch. $$\begin{array}{cccc} {\text { Loom }} \\\hline \mathbf{1} & \mathbf{2} & 3 & \mathbf{4} \\\hline 99 & 97 & 94 & 93 \\97 & 96 & 95 & 94 \\97 & 92 & 90 & 90 \\96 & 98 & 92 & 92\end{array}$$ (a) Write a model for the experiment. (b) Does the loom variance component differ significantly from zero? (c) Comment on the managers' suspicion.

A textile company weaves a certain fabric on a large number of looms. The managers would like the looms to be homogeneous so that their fabric is of uniform strength. It is suspected that there may be significant variation in strength among looms. Consider the following data for 4 randomly selected looms. Each observation is a determination of strength of the fabric in pounds per square inch. $$\begin{array}{cccc} {\text { Loom }} \\\hline \mathbf{1} & \mathbf{2} & 3 & \mathbf{4} \\\hline 99 & 97 & 94 & 93 \\97 & 96 & 95 & 94 \\97 & 92 & 90 & 90 \\96 & 98 & 92 & 92\end{array}$$ (a) Write a model for the experiment. (b) Does the loom variance component differ significantly from zero? (c) Comment on the managers' suspicion.

Probability and Statistics for Engineers and Scientists

One-Factor Experiments: General

Case Study

Questions asked

INSTANT ANSWER

ii) The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is shown below. Assume that the probability that each device functions independently. What is the probability that the circuit operates?

View Answer
 divider
INSTANT ANSWER

If the joint probability density function of random variable \( X \) and \( Y \) is \( f_{X, Y}(x, y)=\left\{\begin{array}{cc}x y, & 0 \leq x \leq 1,0 \leq y \leq 2 \\ 0 & \text { otherwise }\end{array}\right. \), then what is the probability of the event \( A=X^{2}+Y^{2} \leq 1 ? \)

View Answer
 divider
INSTANT ANSWER

Let the continuous random variable \( \mathrm{X} \) denote the current measured in a thin copper wire in milli-amperes. Its cumulative distribution function is given in the following figure. Determine the probability density function of \( \mathrm{X} \).

View Answer
 divider
INSTANT ANSWER

ii) In a semiconductor manufacturing process, two wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent. Let the random variable \( \mathrm{X} \) be the number of contamination particles on a wafer in semiconductor manufacturing. Determine the probability mass function of \( \mathrm{X} \) and find the mean and variance of the random variable \( X \).

View Answer
 divider
INSTANT ANSWER

15. Define \( K \) as the number of under filled bottles from a filling operation in a carton of 24 bottles. Seventy-five cartons are inspected and the following observations on \( X \) are recorded: \( \begin{array}{lllll}\text { Values } & 0 & 1 & 2 & 3 \\ \text { Frequency } & 39 & 23 & 12 & 1\end{array} \) Based on these 75 observations, is a bincmial distribution an appropriate mocel? Perfom a goodness-of-fit procedurs with.5\% LOS.

View Answer
 divider
INSTANT ANSWER

Let \( X \) and \( Y \) denote the proportion of two different chemicals in a sample mixture of chemicals used as an insecticide. Suppose \( X \) and \( Y \) have joint probability density given by: \[ \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\left\{\begin{array}{lc} 2, & 0 \leq \boldsymbol{x} \leq 1,0 \leq \boldsymbol{y} \leq 1,0 \leq \boldsymbol{x}+\boldsymbol{y} \leq 1 \\ 0, & \text { elsewhere } \end{array}\right. \] (Note that \( X+Y \) must be at most unity since the random variables denote proportions within the same sample). a) Find i) \( \mathrm{P}(\mathrm{X}>1 / 2) \) ii) \( \mathrm{P}(\mathrm{Y}<1 / 4) \). b) Find the marginal density functions for \( \mathrm{X} \) and \( \mathrm{Y} \). c) Are \( \mathrm{X} \) and \( \mathrm{Y} \) independent?

View Answer
 divider
INSTANT ANSWER

Express the following extreme values of the joint \( C D F F_{X, Y}(x, y) \) as numbers or in terms of the CDFs \( F_{X}(x) \) and \( F_{Y}(y) \). (1) \( F_{X, Y}(-\infty, 2) \) (2) \( F_{X, Y}(\infty, \infty) \) (3) \( F_{X, Y}(\infty, y) \) (4) \( F_{X, Y}(\infty,-\infty) \)

View Answer
 divider
INSTANT ANSWER

To determine whether there really is a relationship between an employee's performance in the company's training program and his or her ultimate success in the job, the company takes a sample of 400 cases from its very extensive files and obtains the results shown in the following table: \begin{tabular}{ccccc} & \multicolumn{4}{c}{ Performance in training program } \\ & \multicolumn{2}{c}{ Below } & average & Above Average \\ Success in job & Poor & 23 & 60 & 29 \\ (employer's rating) & Average & 28 & 79 & 60 \\ & Very good & 9 & 49 & 63 \end{tabular} Use the 0.01 level of significance to test the null hypothesis that performance in the training program and success in the job are independent.

View Answer
 divider
INSTANT ANSWER

In a true-false test, a test item is considered to be good if it discriminates between well-prepared students and poorly prepared students. If 205 of 250 well-prepared students and 137 of 250 poorly prepared students answer a certain item correctly, test at the 0.01 level of significance whether for the given item the proportion of correct answers can be expected to be at least \( 15 \% \) higher among well prepared students than among poorly prepared students.

View Answer
 divider
INSTANT ANSWER

ii) A company has to choose among three pension plans. Management wishes to know whether the preference for plans independent of job classification. The opinions of a random sample of 1000 employees are shown below: \begin{tabular}{|l|c|c|c|} \hline \multirow{2}{*}{ Job classification } & \multicolumn{3}{|c|}{ Pension Plans } \\ \cline { 2 - 4 } & 1 & 2 & 3 \\ \hline Salaried workers & 182 & 213 & 203 \\ \hline Hourly workers & 154 & 138 & 110 \\ \hline \end{tabular} At \( \alpha=0.05 \), use \( \chi^{2} \)-test to determine whether the preference for pension plans is independent of job classifications?

View Answer
 divider