Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables withμΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 % X1 X2 X3q = 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 normallydistributed random variables withµX1 = 10.4 ; µX2 = 11.8 ; µX3= 11.5Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 %X1 X2 XЗq = (1 0,80,8 1 0,5 |X2 -----> correlation of Matrix0,6 0,5 16X1X3Y < 0; failure occurs 15 şimulations Pf =?. Determine the probability of failure ? (Reliability of Structures)

Given that Y=2X1-2X2+8X2 is normally distributed. Mean of Y=E(Y)= 2*10.4-2*11.8+8*11.5 E(Y)=89.2

Answered: Consider the performance function Y=…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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