Please help with this question (cumulative distribution function of X)

Click For Summary
SUMMARY

The cumulative distribution function (CDF) for the lifetime of a specific electronic device, defined by the probability density function f(x) = 10/x² for x > 10, is F(x) = 1 - 10/x for x > 10. To find P(X > 20), substitute 20 into the CDF, yielding P(X > 20) = 1 - F(20) = 0.75. Additionally, the probability that at least 3 out of 6 devices function for at least 20 hours can be calculated using the binomial distribution formula, assuming independence among devices.

PREREQUISITES
  • Understanding of probability density functions (PDF) and cumulative distribution functions (CDF)
  • Familiarity with binomial distribution and its applications
  • Basic knowledge of calculus for integration and differentiation
  • Experience with statistical software or tools for probability calculations
NEXT STEPS
  • Study the derivation of cumulative distribution functions from probability density functions
  • Learn about the binomial distribution and its applications in reliability engineering
  • Explore statistical software like R or Python for performing probability calculations
  • Investigate the concept of independence in probability and its implications for device lifetimes
USEFUL FOR

Statisticians, data analysts, reliability engineers, and anyone involved in the analysis of electronic device lifetimes and performance probabilities.

tiffyuyu
Messages
2
Reaction score
0
The probability density function of the lifetime of a certain type of electronic device
(measured in hours), X, is given by

f(x) = 10/x^2,
0,
x > 10;
elsewhere.

(a) Find the cumulative distribution function of X, namely F(x) and hence find
P(X > 20).
(b) What is the probability that of 6 such devices, at least 3 will function for at least 20 hours? What assumption did you make?
 
Physics news on Phys.org
There are characters in your post that need to be edited, and can you show what you have done so far so our helpers see where you are stuck?
 

Similar threads

Undergrad Calculating the inverse of a function involving the error function
  • · Replies 3 ·
Replies
3
Views
2K
Graduate A different discrete normal distribution
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Does the generalized gamma distribution have a mgf?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Distribution and Density functions of maximum of random variables
  • · Replies 6 ·
Replies
6
Views
5K
MHB Cdf, expectation, and variance of a random continuous variable
  • · Replies 1 ·
Replies
1
Views
2K
MHB Cumulative distribution function
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Separation of variables for Named Probability Density Distributions
  • · Replies 4 ·
Replies
4
Views
1K
MHB Computing joint cumulative distribution function
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Hypergeometric Distribution Calculation in Libreoffice
  • · Replies 2 ·
Replies
2
Views
2K
MHB Integral limits when using distribution function technique
  • · Replies 10 ·
Replies
10
Views
2K