# Tagged Questions

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### generating random samples with a PDF

I have the PDF of a distribution from which it is not possible to get a closed from for the CDF or inverse CDF. Is there a technique that would allow me to generate samples from this distribution ...
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### Unconditional sampling distribution of regression coefficients

I am trying to find the (unconditional) sampling distribution of a regression coefficient in a simple linear regression. The linear regression $Y = \beta_0 + X\beta_1 + \epsilon$ is conducted for $N$ ...
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### To sample or not to sample?

I have the following issue (I want to predict sports results). Let $X$ be a discrete RV with $m$ possible outcomes, each having probability $p_i$, for $i=1,\ldots,m$. Assume that I have a large iid ...
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### Probability in a Random Sample [closed]

V. The mean monthly rental rate for a two-bedroom apartment in Atlanta is $\$982$(Elle. September 1998). Assume that the population mean is$\mu = \$982$ and the population standard deviation is ...
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### Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
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### Confidence/Tolerance interval for a percentage of a population

I have a problem I'm not sure how to solve. It goes something like: ...
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### How can I sample a bivariate Gaussian distribution using Gibbs sampling?

I'm trying to sample a bivariate Gaussian distribution using Gibbs sampling, but I think I don't have the correct conditional probabilities. According to this lecture slides, the conditional ...
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### Survey vs interview size

I have a survey of size 120 and 20 interviews. Can I compare the results? Both groups answered same questions. Example: let's say a question was do you like to read novels ? Can I say that 20% of ...
### Proof that $\frac{(\bar X-\mu)}{\sigma}$ and $\sum_{i=1}^n\frac{(X_i-\bar X)^2}{\sigma^2}$ are independent
Let $X_i\sim N(\mu,\sigma^2)$ ; where$[i=1,2,\ldots,n]$ $Z_i\sim N(0,1)$ ; where$[i=1,2,\ldots,n]$ Proof that $\bar Z=\frac{(\bar X-\mu)}{\sigma}$ and \$\sum_{i=1}^{n}(Z_i-\bar ...