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Recent questions in Modeling data distributions

Reggie 2021-01-23

The article “Stochastic Modeling for Pavement Warranty Cost Estimation” (J. of Constr. Engr. and Mgmnt., 2009: 352–359) proposes the following model for the distribution of Y = time to pavement failure. Let $\displaystyle{X}_{{{1}}}$ be the time to failure due to rutting, and $\displaystyle{X}_{{{2}}}$ be the time to failure due to transverse cracking, these two rvs are assumed independent. Then $\displaystyle{Y}=\min{\left({X}_{{{1}}},{X}_{{{2}}}\right)}$. The probability of failure due to either one of these distress modes is assumed to be an increasing function of time t. After making certain distributional assumptions, the following form of the cdf for each mode is obtained: $\displaystyle\Phi{\left[\frac{{{a}+{b}{t}}}{{\left({c}+{\left.{d}{t}\right.}+{e}{t}^{{{2}}}\right)}^{{\frac{{1}}{{2}}}}}\right]}$ where $\Uparrow \Phi$ is the standard normal cdf. Values of the five parameters a, b, c, d, and e are -25.49, 1.15, 4.45, -1.78, and .171 for cracking and -21.27, .0325, .972, -.00028, and .00022 for rutting. Determine the probability of pavement failure within $\displaystyle{t}={5}$ years and also $\displaystyle{t}={10}$ years.

a2linetagadaW 2021-01-23

Give a complete and correct answer to the question asked what Posterior Probabilities?

naivlingr 2021-01-19

Answer the following true or false. If false, explain why. a. We can reduce $α$ (alpha) by pushing the critical regions further into the tails of the distribution. b. A decrease in the probability of the type II error always results in an increase in the probability of the type I error, provided that the sample size n does not change. c. The p-value of a left-sided hypothesis test is always half of a two-sided hypothesis test.

Cem Hayes 2021-01-19

Which possible statements about the chi-squared distribution are true?
a) The statistic $X^{2}$ , that is used to estimate the variance $S^{2}$ of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.

pancha3 2021-01-17

Use the table from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places. $P (x = 3) = ?$
$P (1 < x < 4) = ?$
$P (x \geq 8) = ?$ Use the data from the Organize the Data section to calculate the following answers. Round your answers to four decimal places. $R F (x = 3) = ?$
$R F (1 < x < 4) = ?$
$R F (x \geq 8) = ?$ Discussion Questions 1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical, empirical, and simulation distributions. Use complete sentences.

Line 2021-01-16

To find: The function that models the area of rectangle in terms of length of one of its sides. The perimeter of rectangle is 20 ft.

Daniaal Sanchez 2021-01-13

A kickball's height h (in feet) t seconds after it is kicked off the ground is represented by the function $h = - 16 t^{2} + 48 t$ (in math terms). Calculate the kickball's highest point. b) Locate and examine the symmetry axis.

Caelan 2021-01-10

In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger compartments. By 1990, Florida had passed such a law, but Georgia had not.
(i) Suppose you can collect random samples of the driving-age population in both states, for 1985 and 1990. Let arrest be a binary variable equal to unity if a person was arrested for drunk driving during the year. Without controlling for any other factors, write down a linear probability model that allows you to test whether the open container law reduced the probability of being arrested for drunk driving. Which coefficient in your model measures the effect of the law?
(ii) Why might you want to control for other factors in the model? What might some of these factors be?
(iii) Now, suppose that you can only collect data for 1985 and 1990 at the county level for the two states. The dependent variable would be the fraction of licensed drivers arrested for drunk driving during the year. How does this data structure differ from the individual-level data described in part (i)? What econometric method would you use?

UkusakazaL 2021-01-07

A store sells custom circular rugs. The table shoes the costs c(in dollars) of rugs that have diameter's of d feet. Let the diameter d represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or quadratic function.

Dottie Parra 2021-01-06

A weather forecaster predicts that the temperature in Antarctica will decrease $8^{\circ} F$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least $36^{\circ} F$

DofotheroU 2021-01-05

In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give example of population members that might have been omitted.
a) The population consists of all 250 students in your laege statistics class. You plan to obtain a sample random sample of 30 students by using the sample frame of students present next Monday.
b) The population consists of all 15-year-olds living in the attendance district of a local high school. You plna to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame.

Ayaana Buck 2021-01-02

The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (Water Research, $1984: 1169-1174$ ) suggests the uniform distribution on the interval (7.5,20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.
What are the mean and variance of depth?
b. What is the cdf of depth?
What is the probability that observed depth is at most 10? Between 10 and $15 ?$
What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

fortdefruitI 2020-12-31

The perimeter of a triangular plot of land is 2400ft. The longest side is 200 ft less than twice the shortest. The middle side is is 200 ft ,ess than the longest side. Finde the lengths of the three sides of the triangular plot

shadsiei 2020-12-30

The tables show the battery lives (in hours) of two brands of laptops. a) Make a double box-and-whisker plot that represents

BenoguigoliB 2020-12-29

Regarding z-scores: a. How is a z-score obtained? b. What is the interpretation of a z-score? c. An observation has a z-score of 2.9. Roughly speaking, what is the relative standing of the observation?

Chardonnay Felix 2020-12-28

The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city. $\begin{array}{cc} P o p u l a t i o n (t h o u s a n d s) & W a l k i n g S p e e d (f e e t p e r s e c o n d) \\ 5.5 & 0.6 \\ 14 & 1.0 \\ 71 & 1.6 \\ 138 & 1.9 \\ 342 & 2.2 \end{array}$

Khaleesi Herbert 2020-12-27

The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by $\hat{y} = - 4815 + 3.765 x .$ A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: $(2003, 2736), (2004, 2715), (2007, 2675), (2009, 2719), (2013, 270)$ . All coordinates are approximate. Interpret the y-intercept of the least squares regression line. Is it feasible? Select the correct answer below: The y-intercept is −4815, which is not feasible because a product cannot have a negative cost. The y-intercept is 3.765, which is not feasible because an expensive product such as a designer jacket cannot have such a low cost. The y-intercept is −4815, which is feasible because it is the value from the regression equation. The y-intercept is 3.765 which is feasible because a product must have a positive cost.

Braxton Pugh 2020-12-25

True or false to each of the statements in parts (a) and (b), and explain your reasoning. a. Two data sets that have identical frequency distributions have identical relative-frequency distributions. b. Two data sets that have identical relative-frequency distributions have identical frequency distributions. c. Use your answers to parts (a) and (b) to explain why relativefrequency distributions are better than frequency distributions for comparing two data sets.

Wierzycaz 2020-12-25

What is enterprise data modeling?

melodykap 2020-12-14

A standard $3 σ x - \overset{―}{}$ chart has been enhanced with early warning limits at plus-minus one $σ$ from the centerline . Three sample means in a row have plotted above the $+ 1 σ$ line . what is the probability of this happening if the process is still in control.

Statistics and probability also include various data modeling questions, which can be encountered basically everywhere from Social Sciences and Biology to Engineering and Data Science. Depending on your questions, you can receive immediate help by looking through the data modeling examples that we have presented below for you. These will help you to find solutions and find the answers to presented challenges. It is recommended to model your data carefully and to check things twice to ensure that everything is correct because accuracy is the key to any statistical work where a calculation is involved.

Data Modeling Examples and Frequently Asked Questions