Purchase Solution

# Mathematical Statistics by Bain Engelhardt

Not what you're looking for?

(See attached file for full problem description with proper symbols)

We are using the book introduction to probability and mathematical statistics by Bain Engelhardt

---
6.32 A system is composed of five independent components connected is series.
a) If the pdf of the time to failure of each component is exponential, ,
then give the pdf of the time to failure of the system.
b) Repeat a) but assume that the components are connected in parallel.
c) Suppose that the five-component system fails when at least three components fail.
Give the pdf of the time to failure of the system.
d) Suppose that independent components are not distributed identically, but rather
. Give the pdf of the time to failure of a series system in this case.
--

##### Solution Summary

This Solution contains calculations to aid you in understanding the Solution to these questions.

##### Solution Preview

6.32 A system is composed of five independent components connected is series.
a) If the pdf of the time to failure of each component is exponential, ,
then give the pdf of the time to failure of the system.

Solution. Denote by the time to failure of the ith component. By hypothesis, independently.

So,

Note: Since , their identical pdf is

If a system is composed of five independent components connected is series, then the time X to failure of the system is the least time, namely,

So,
...

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.