# 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.

5,977 questions
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### Partitioned regression model: estimator of beta 1

below is an exercise that is really giving me a hard time, I believe that there is a simple way around it but I can not find it: Assume the correct regression model is Y = X$\beta$ + $\epsilon$ for E(...
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### How to change in y variable having means, standard deviations, and correlation coefficient?

The following statistics have been obtained by using the data of money supply growth rate and inflation rate for the last 30 years. The average money supply growth rate, its standard deviation,...
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### Formula for Power of Upper Tail Sign Test

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_A: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
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### Statistics and Probability. Please show solution [closed]

Miss Romero noted that the mean scores of a random sample of 15 grade 8 students who had taken a special test were 80.5. If the standard deviation of the scores was 3.1 and the sample came from an ...
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### Odds Ratio Vs. Risk Ratio

Relative risk, odds ratio, risk ratio, risk difference - these are all measures of the direction and the strength of the association between two categorical variables. Can I use any of these four ...
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### Constant Variance Assumption in Linear Regression

It seems to me that the following plot of "Residuals Vs. Fitted Values" violates the assumption of constant variance, since for lower fitted values, there are fewer points whereas for higher fitted ...
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### Expected value using indicator variable

Suppose that $8$ white balls and $2$ black balls will be randomly ordered, from left to right (with all permutations of the $10$ balls equally likely), what is the expected value of the number of ...
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### Question regarding conditional expectation [duplicate]

In Larry Wasseman's lecture notes(lecture 4, page 4) I found this statement $\mathbb{E}[Y|X=x] = \sum_y y f_{Y|X}(y|x)$ or $=\int_y y f_{Y|X}(y|x)dy.$ An important point about the conditional ...
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### Find a copulas given joint distribution

We were given some homework to complete and would like to know how do you calculate the copulas I know from the definition that: C(X,Y)=FX,Y(Fx^-1, Fy^-1) and ill have to find the marginals by ...
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### Are there situations where improper priors can be avoided via a prior on a subset of the real line and a transformation?

There are many situations where improper priors are "permissable" (Berger, 2009). In many cases, these improper priors are improper because they are "flat" on the real line. A well known example is ...
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### Confidence Interval help

2 1 The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows: 458, 450, 457, 456, 460, 459, 458, 456 a) ...
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### Algebraic Manipulations in Mann-Whitney-Wilcoxon Test Statistics

Given Let $\Delta > 0$ be positive real number. Consider the Wilcoxon-Mann-Whitney upper tail test $H_0: \Delta \leq 0 \,\,\, \text{vs} \,\,\, H_a: \Delta > 0$ aimed at testing the difference ...
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### Poisson question that I can’t solve [closed]

1.Customers arrive at a bank at a poisson rate. Suppose that two customers arrived during the first hour. What is the probability that (A) both arrived during the first $20$ minutes? (B) at least ...
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### Rao-Blackwellization in variational inference

The Black box VI paper introduces Rao-Blackwellization as a method to reduce the variance of the gradient estimator using score function, in section 3.1. However I don't quite get the basic idea ...
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### Question regarding independence of events

I am reading Wasserman's book and his class notes. In the notes, I found the following statement If A, B are disjoint, both having positive probability, then A and B cannot be independent. Now, if ...
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### Conditional Probability - Drawing balls from an urn

I have that question from a past exam (without answer): There are two urns, say I and II. Urn I contains 1 white ball and 1 black ball. Urn II containts two white balls and 3 black balls, and suppose ...
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### Gamma Distribution Sufficient Statistics

I've been asked to show the gamma distribution can be written in the form $p(x|\alpha, \beta) = f(x) g(\alpha, \beta) e^{h(\alpha,\beta)^T T(x)}$ where $T(x)$ is a sufficient statistic. .... I have ...
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### Bayes Rule Bayesian Risk and Decision

Good day, When attempting this problem I came across some difficulties. A humanitarian charity wishes to classify a village as being at either high or low risk of flooding. The following ...
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### Uniform distribution on the simplex. - Thomas cover

I'm trying to formulate the solution for the following problem: I was thinking in finding the equivalent distribution on $X_i$ based on $Y_i$, but I think I'm cheating. I think that the autor wants ...
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### Help with centered multiple linear models

For the multiple linear model in centered form prove that where is the L-2 norm, defined as Any help would be greatly appreciated. Perhaps links to papers, chapters, websites that could help me ...
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### How can I test this distribution?

Say I have 40 people that are sorted into 20 pairs. Out of the 40 people, 20 are A People and 20 are B People. I want to see if the distribution of A People and B People is random. For example, if it ...
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### Different solution for a probability question

I got the following problem: Find the probability that for two arbitrary numbers $x$ and $y$ with $x,y \in [0,1]$ they satisfy $x+y<1$ and $xy<\frac1{10}$. In short words the sum of the two ...
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### Random variables - proof of convergence in probability

I've got this exercise from lecture notes, but I couldn't find an answer. For each positive integer $n$, let $X_{n}$ be a non-negative random variable with $\mathbb{E}[X_{n}] < \infty$. Prove that ...
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### Need help with Least Squares Estimator

I am interested in a One-Way ANOVA model:                           &...
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### Summation Bounds When Finding Transformation of 2 Poisson Random Variables

I am reviewing some material on functions of several random variables from Section 7.4 of John E. Freund's Mathematical Statistics, 6th Edition, and I'm stumped on how the author gets the upper bound ...