- #1
EvLer
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How do I approach finding variance of sample mean of Poisson distribution?
thanks.
thanks.
Finding Variance of Sample Mean of Poisson Distribution
In summary, the conversation discusses the approach to finding the variance of the sample mean for a Poisson distribution. The definition of variance is mentioned, but there is confusion about applying it to the sample mean. The formula for calculating the sample variance is also mentioned, along with the fact that for a Poisson distribution, the mean and standard deviation are equal to the parameter lambda.
- #2
radou
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EvLer said:
You can certainly start with looking at the definition of variance.
- #3
EvLer
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I did: Var(X) = E(X2) - (E(X))2
the problem is that this is given for rv X, not X' or X-bar, that's where i get lost.
I know that last term is lambda2.
Actually what I need to find for this problem is E(X'2), i.e.
E(X'2) = Var(X') + lambda2
the problem is that this is given for rv X, not X' or X-bar, that's where i get lost.
I know that last term is lambda2.
Actually what I need to find for this problem is E(X'2), i.e.
E(X'2) = Var(X') + lambda2
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- #4
EvLer
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ok, last question, pleeeease some one look 
i can't find much on this anywhere and the book does not say much... i don't have intuition for these things...
can I say that sample variance is sum(lambda)/n?
I found something that said sample variance is Sum(Var[X]) of whatever it is the RV divided by n...
i can't find much on this anywhere and the book does not say much... i don't have intuition for these things...can I say that sample variance is sum(lambda)/n?
I found something that said sample variance is Sum(Var[X]) of whatever it is the RV divided by n...
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- #5
radou
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According to my old lecture notes, the sample variance for (X1, ..., Xn) is defined with [tex]\frac{1}{n} \sum_{i=1}^n(X_{i}-\overline{X})^2[/tex], where [tex]\overline{X} = \frac{1}{n}\sum_{i=1}^n X_{i}[/tex] , and, in your case X~P(lambda).
- #6
HallsofIvy
Science Advisor
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Yes, the Poisson distribution depends on a single parameter and has the property that both mean and standard distribution are equal to that parameter.
FAQ: Finding Variance of Sample Mean of Poisson Distribution
1. What is the formula for finding the variance of the sample mean of a Poisson distribution?
The formula for finding the variance of the sample mean of a Poisson distribution is Var(X̄) = λ/n, where λ is the mean of the Poisson distribution and n is the sample size.
2. How is the sample mean of a Poisson distribution different from the population mean?
The sample mean of a Poisson distribution is calculated from a subset of the population, while the population mean is calculated from the entire population. The sample mean is a random variable, while the population mean is a fixed value.
3. Can the sample mean of a Poisson distribution be negative?
No, the sample mean of a Poisson distribution cannot be negative. This is because the Poisson distribution is bounded at zero and has a positive skew, so the sample mean will always be a positive value.
4. How does increasing the sample size affect the variance of the sample mean of a Poisson distribution?
As the sample size increases, the variance of the sample mean decreases. This is because a larger sample size provides more accurate estimates of the population mean, resulting in a smaller spread of sample means around the population mean.
5. Can the variance of the sample mean of a Poisson distribution be larger than the population mean?
Yes, the variance of the sample mean of a Poisson distribution can be larger than the population mean. This is possible when the sample size is small and there is a large amount of variability in the population. As the sample size increases, the variance of the sample mean will approach the population mean.