Jointly Distributed Random Variables : Gamma and Exponential Distributions
Not what you're looking for?
If X1, X2,...Xn are all independent Expo(λ), and Sn=Σ i=1..n Xi, then Sn≈Gamma (n,λ). Show that this is true when n=2.
Please see attached.
Purchase this Solution
Solution Summary
Gamma and Exponential Distributions with regard to Jointly Distributed Random Variables are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
(This problem is from the chapter of Jointly Distributed Random Variables.)
Before I prove this question, I would like to recall the Exponential random variable and Gamma distribution.
A random variable is said to have a gamma distribution with parameters if its density function is
...
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!"
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts