Determination of a Join pdf

In summary, the joint pdf of the durations of a set of n bulbs with an exponential distribution is given by f(t_1,t_2...t_n)=\lambda^n e^{-\lambda \sum_{i=1}^{n}t_i}. This assumes that the durations are independent.
  • #1
Gp7417
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Determination of a Joint pdf

Hi all! Someone can help me with this problem?

The duration of a certain type of bulbs has a exponential distribution with known parameter [tex]\lambda [/tex]. Consider a set of n bulbs. Which is the joint pdf of the durations [tex]t_{i}[/tex] of the [tex]n[/tex] bulbs?
 
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  • #2
Can you assume that the durations' distributions are independent? If so, there shouldn't be a problem.
 
  • #3
Yes the durations can be indipendent.
 
  • #4
What do you know about distributions of independent random variables?
 
  • #5
Is this the right answer?
[tex]f(t_1,t_2...t_n)=\lambda^n e^{-\lambda \sum_{i=1}^{n}t_i}[/tex]
 

1. How do you determine the join pdf for a multivariate distribution?

The join pdf for a multivariate distribution can be determined by taking the product of the individual pdfs of each variable. This is known as the joint probability distribution function.

2. What is the purpose of determining the join pdf?

Determining the join pdf allows scientists to understand the relationship between multiple variables in a distribution. This can help in making predictions and analyzing data.

3. How is the join pdf calculated for continuous variables?

For continuous variables, the join pdf is calculated by integrating the joint probability distribution function over the entire range of all variables. This results in a single value representing the probability of the event.

4. Can the join pdf be used to find the probability of a specific event?

Yes, by plugging in the values of the variables into the joint probability distribution function, the probability of a specific event can be calculated.

5. Are there any limitations to using the join pdf in data analysis?

One limitation is that it assumes all variables are independent of each other, which may not always be the case in real-world scenarios. Additionally, the join pdf can become computationally intensive for large datasets with many variables.

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