Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables with μΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5 Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 % X1 X2 X3 q = 1 0,8 6 X1 0,8 1 0,5 X2 -----> correlation of Matrix 0,6 0,5 1 X3 Y < 0; failure occurs 15 simulations Pf =? . Determine the probability of failure ? (Reliability of Structures)

Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables with μΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5 Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 % X1 X2 X3 q = 1 0,8 6 X1 0,8 1 0,5 X2 -----> correlation of Matrix 0,6 0,5 1 X3 Y < 0; failure occurs 15 simulations Pf =? . Determine the probability of failure ? (Reliability of Structures)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Consumer Reports rated airlines and found that 79% of the flights involved in the study arrived on…

A: Let X be the number that will arrive on time from binomial distribution with probability (p) = 79%…

Q: Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the…

A: From the given information, Consider, X and Y be independent random variables,…

Q: Suppose a Major League Baseball player’s yearly batting average is, on average,0.200* with variance…

Q: Researchers working for a sports drink company would like to know if a new blend if its popular…

A: Given data : sample size, n = 20 sample mean, x̄ = 270.0 sample standard…

Q: To obtain a maximum amount of variance, an item ought to have a degree of difficulty of what?

A: To obtain a maximum amount of variance an item ought to have a degree of difficulty is the number of…

Q: sample of n=25 college students was given problem solving task at noon one day and again at noon the…

Q: The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the…

A: The random variable is the maximum weightThe random variable is the time The correlation…

Q: The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose…

Q: An electrical firm manufactures light bulbs that have a length life with normal distribution, and…

A: Since the population of the life time of the light bulbs being sampled from following a normal…

Q: The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the…

A: Firstly, correlation coefficient ($ r $) measures the strength and direction of the linear…

Q: Perform a a Pearson’s correlation in SPSS to determine whether the weight of an automobile…

A: Note: Hi there! Thank you for posting the question. As the data corresponding to the variables…

Q: The following table shows the results of two random samples that measured the average number of…

A: Solution: Given information: n1=17 Sample size of Li-ion n2= 14 Sample size of NiMH

Q: In one of the New York City parks, there has been a problem with muggings in the summer months. A…

A: The regression equation is and want to calculate the correlation coefficient

Q: What is the critical value at a .01 significance level? (Notes: enter only the positive value if…

A: The degrees of freedom is, df=n1+n2-2=27+30-2=55 The degrees of freedom is 55. The significance…

Q: A manufacturing company is interested in buying one of two different kinds of machines for…

Q: An examination in biology has been taken by biology majors and also by some students from other…

A: Given:

Q: Solve this part independently). A random sample of 6 National bank employees was taken to help…

A: Given : Sample size (n) = 6 Sample data (X) : 13 , 5 , 6 , 10 , 7 , 12 ∑X = 53 Sample variance (S2)…

Q: (IN SAS) Reconsider the 'NBAPPG2008' data. Find a variable that seems to be normally distributed. If…

Q: observe the efficiency of students to see whether students do better when they study all at once or…

A: The objective is to check whether the mean test scores of the two groups significantly differ at the…

Q: Two groups of mice were injected with a measured amount of tumor pulp. The first group of 27 mice…

A: It is a Left tailed test.

Q: An examination in biology has been taken by biology majors and also by some students from other…

Q: A set of solar batteries is used in a research satellite. The satellite can run on only one battery,…

A: Let X be the life time of the battery in months n = sample size = 30 s2 = Sample variance = 15.4…

Q: You want to run a 2-tailed independent t-test on sample 1 (M = 24.3, SD = 1.6) and sample 2 (M =…

A: Given, The test is 2 tailed independent samples t-test. Sample 1 has mean X1=24.3, standard…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

100%

Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables with

μΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5
Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 %

X1 X2 X3
q = 1 0,8 6 X1
0,8 1 0,5 X2 -----> correlation of Matrix
0,6 0,5 1 X3

Y < 0; failure occurs 15 simulations Pf =?

. Determine the probability of failure ? (Reliability of Structures)

Consider the performance function Y= 2X1-2X2+8X3 are all normally
distributed random variables with
µX1 = 10.4 ; µX2 = 11.8 ; µX3= 11.5
Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 %
X1 X2 XЗ
q = (1 0,8
0,8 1 0,5 |X2 -----> correlation of Matrix
0,6 0,5 1
6X1
X3
Y < 0; failure occurs 15 şimulations Pf =?
. Determine the probability of failure ? (Reliability of Structures)

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Two groups of mice were injected with a measured amount of tumor pulp. The first group of 27 mice was given a high dosage of chemotherapy while the second group of 30 mice was given a low dosage of chemotherapy. After forty days, the first group had an average tumor size of 0.51cc with a variance of 0.10; the second group had an average tumor size of 0.64cc with a variance of 0.045. Were the tumor sizes of group 1 significantly smaller than those of group 2? What is the observed test statistic?
Explain Distribution of the F-Statistic using the homoskedasticityonlyestimator of the covariance matrix?
Define the Distributed Lag Model with Additional Lags and AR(p) Errors?
Captopril is a drug designed to lower systolic blood pressure. In a trial, 12 randomly selected subjects were treated with the drug and another 12 randomly selected subjects were treated with the placebo. Assume the two populations are normally distributed. The results and some summary statistics are shown in the table. Note that some of the summary statistics may not be useful or relevant! Data Group Placebo 200 174 198 170 179 182 193 209 185 155 169 210 (ž1 = 185.3) (s1 = 17.1) Captopril (I2 = 166.8) (s2 = 14.9) d = I1 – 12 (d = 18.6) (sa = 10.1) %3D %3D 191 170 177 167 159 151 176 183 159 145 146 177 9. 4 21 3 20 31 17 26 26 10 23 33 %3D data %3D Using a 0.01 significance level, is there sufficient evidence to support the claim that the mean systolic blood pressure is lower for those treated with the drug than for those treated with the placebo? Use the p-value method. For full marks, include a diagram of the distribution indicating important components of the question.
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance o of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of o2 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 15.4 months (squared). Using a 0.05 level of significance, test the claim that o? = 23 against the claim that o is different from 23. (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit months upper limit…
The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.
The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the times (in seconds) to run a 10-meter sprint for 12 international soccer players are shown in the attached data table with a sample correlation coefficient r of -0.971. A 13th data point was added to the end of the data set for an international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 2.01 seconds. Describe how this affects the correlation coefficient r. Use technology. Click the icon to view the data set. The new correlation coefficient r going from -0.971 to (Round to three decimal places a gets stronger, gets weaker, stays the same,
Consider the model (1-B)(1-0.2B)X_t = (1-0.5B)W_t find the forecasts for one, two and three steps ahead and calculate the variance of the one, two, and three steps ahead forecast errors