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5 questions
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136
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Sampling distribution of exponential sample variance (formal not empirical)
Addressing this problem:
Let $X_1, ..., X_n$ be iid exp($\theta$) with pdf,
$f(x)=\frac{1}{\theta}e^{-\frac{x}{\theta}}$. What is the distribution of the sample variance?
This is to be done by ...
0
votes
0
answers
17
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Sampling Distribution of Exponential Sample Variance (Formal, not Empirical) [duplicate]
Addressing this problem:
Let X1,...,Xn be independent identically distributed exponential variables with parameter θ, i.e. with pdf, f(x)=(1/θ)*exp(−x/θ). What is the distribution of the sample ...
2
votes
1
answer
396
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If X~Exp(λ), what is the expected value of Y=X²?
I am trying to compute this using the integral definition of expected value but I don't think I am doing it right as I am getting a very hard integral that I can not solve.
When computing $\mathbb{...
3
votes
2
answers
394
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Variance of a function of the sample variance
I'm looking for the sampling standard deviation of $\hat\sigma^\gamma$, where $\hat\sigma$ is a sample standard deviation. For simplicity, lets do the sample variance of the sample variance and take ...
5
votes
1
answer
6k
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What is the expectation of exponential of the product of two random variables?
I am looking for examples of probability distributions that would allow me to characterize the distribution (at least approximately) and to compute the first two moments exactly of:
$$
e^{aXY}
$$
...