# Questions tagged [self-study]

A routine exercise from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

644 questions
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### Question on how to normalize regression coefficient

Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares. Suppose you have $y=\beta_0+\beta_1x_1$, ...
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### Functions of Independent Random Variables

Is the claim that functions of independent random variables are themselves independent, true? I have seen that result often used implicitly in some proofs, for example in the proof of independence ...
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### How are regression, the t-test, and the ANOVA all versions of the general linear model?

How are they all versions of the same basic statistical method?
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### Construction of Dirichlet distribution with Gamma distribution

Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
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### $P[X=x]=0$ when $X$ is continuous variable

I know that for continuous variable $P[X=x]=0$. But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?
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### Expected Value and Variance of Estimation of Slope Parameter $\beta_1$ in Simple Linear Regression
I am reading a text, "Probability and Statistics" by Devore. I am looking at 2 items on page 740: the expected value and variance of the estimation of $\beta_1$, which is the slope parameter in the ...