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3
questions
4
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2
answers
310
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For non-normally distributed random variables, why does $[\mu - 1.96 \sigma, \mu + 1.96 \sigma]$ contain $\approx$ 95% of the distribution?
My question is, if you take a random variable $X$ with an arbitrary distribution, which has a known and well defined mean & variance, then why does the following interval contain $\approx 95\% $ ...
- 810
2
votes
2
answers
132
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Computing the confidence interval for two samples but getting slightly different answers
Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
- 43
4
votes
1
answer
2k
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How can I obtain the 95% confidence interval for the variance of a random effect?
After running a linear mixed model, I want to obtain the 95% confidence interval for the variance estimation of my random effect. The function confint() in R gives ...
- 315