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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 ...
R. Story's user avatar
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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 ...
R. Story's user avatar
2 votes
1 answer
396 views

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{...
klw_123's user avatar
  • 61
3 votes
2 answers
394 views

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 ...
generic_user's user avatar
  • 13.7k
5 votes
1 answer
6k views

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: $$ e^{aXY} $$ ...
PatrickT's user avatar
  • 157