Probability Density Function Help

In summary, the conversation discusses the probability density function for the time to failure of an electric component and how to determine the probability that the component lasts more than 1000 hours before failure. It is suggested to integrate the given function from [1000, infinity] to solve this. The conversation also mentions determining the number of hours at which 10% of all components have failed, which can be solved by finding when the probability of failure is .10.
  • #1
Mesmer
40
0
Probability Density Function...Help

The probabiltiy density function of the time to failure of an electric component in hours is [tex]f(x)=e^{(-x/3000)/3000}[/tex] for x > 0 and f(x) = 0 for [tex] x \leq 0[/tex] determine the probability that

a) A component last more than 1000 hours before failure
I know how to solve this part. All I have to to is integrate the given function from [1000, infinity].

But how do determine the number of hours at which 10% of all the components have failed? I don't know what interval I should integrate over. Any Ideas?
 
Last edited:
Physics news on Phys.org
  • #2
If F(x) is the probability that a component has failed by time x, you are looking for when F(x) = .10. Can you solve that?
 
  • #3
yes I can. thank you!
 
  • #4
when I solve it as you state that is no the answer.
any other ideas?
 

1. What is a probability density function (PDF)?

A probability density function, or PDF, is a mathematical function that describes the probability of a random variable taking on a certain value or falling within a certain range of values. It is often used to model continuous random variables, such as the height or weight of a population.

2. How is a probability density function different from a probability distribution function?

A probability density function is a function that describes the probability of a continuous random variable taking on a certain value, while a probability distribution function describes the probability of a discrete random variable taking on a certain value. In other words, a PDF measures the likelihood of a value occurring within a range, while a PDF measures the likelihood of a specific value occurring.

3. How do you calculate the area under a probability density function curve?

The area under a probability density function curve represents the total probability of all possible outcomes. To calculate this area, you can use the integral calculus technique of integration. Simply integrate the PDF function over the desired range of values to find the total probability.

4. What is the relationship between a probability density function and a cumulative distribution function?

A cumulative distribution function (CDF) is the integral of a probability density function. It represents the probability that a random variable is less than or equal to a certain value. In other words, the CDF is the area under the PDF curve up to a given point. By taking the derivative of the CDF, you can obtain the PDF function.

5. How is a probability density function used in statistical analysis?

A probability density function is a crucial tool in statistical analysis, as it allows us to model and understand the behavior of continuous random variables. It can be used to calculate important metrics such as mean, variance, and standard deviation, and can also be used to make predictions about the likelihood of certain outcomes occurring. It is also used in hypothesis testing and creating confidence intervals.

Similar threads

Probability density function of Z=X+Y and Z=XY
    • Calculus and Beyond Homework Help
Replies
19
Views
959
Probability Density Functions: Transformation of Variables
    • Calculus and Beyond Homework Help
Replies
3
Views
995
Finding marginal distribution of 2d of probability density function
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Finding Probability Density Functions for Independent Random Variables
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Probability density function for a given problem
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Probability Density of ##x## (Wiener Process)
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Probability Density Function problem
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
A Constructing PDFs for Max Likelihood Density Estimation Problem
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
Probability: Prior Distribution for a Continuous Variable
    • Calculus and Beyond Homework Help
Replies
1
Views
571
Finding k in a probability density function
    • Calculus and Beyond Homework Help
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top