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.

5,850 questions
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Prove bi-directional relationship between convergence in distribution and convergence of probability mass functions

Let $X$ be a random variable that is positive and integer-valued. Let $X_1, X_2, ...$ also be random variables that are positive and integer-valued. Prove that $X_n$ converges in distribution to $X$ ...
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Why divide by 1-leverage?

I'm reading about resampling methods, and specifically leave-one-out cross-validation. I understood the method, and how to calculate the estimate of the test MSE (Mean squared error): In the setup ...
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Which test to use from a paired data that has only 4 cases of information from each group

I have a question from an exam: A Statistics Professor believes that adding videos of statisticians consulting on applied problems to her standard instructional material will help students solve ...
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How to prove the concentration equality for standard normal?

The following inequality is given in some of Yale's online lecture notes $$P(|Z|>x) \leq 2 \sqrt{2 \pi} \phi(x)$$ Where $Z \sim N(0,1)$ with density $\phi(x)$. They call it a concentration ...
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Confused with What Kind of Test I Should be Using

I have a question from an exam: The chef rates the taste quality of 5 different brands of anchovies. The brands came packaged in both a jar and a can. The chef rates 10 combinations of brand/...
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How to get standard deviation when the only given information is sample mean and p-value

I have a question for an exam: You read a journal article on TOTAL-cholesterol, HDL-cholesterol and LDL-cholesterol from a study of n=100 patients where TOTAL-cholesterol = HDL + LDL cholesterol. ...
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Prove that the sum and the absolute difference of 2 Bernoulli(0.5) random variables are not independent

Let $X$ and $Y$ be independent $Bernoulli(0.5)$ random variables. Let $W = X + Y$ and $T = |X - Y|$. Show that $W$ and $T$ are not independent. I know that I have to show that $P(W, T)$ is not equal ...
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Type 1 and Type 2 errors trade-off

Reducing Type 1 error will always result in increasing the Type 2 error This statement is false. I understand the definitions of Type 1 and Type 2 errors. What I understand is that there is, in fact, ...
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Find joint distribution for two different cases Kruskal Wallis

I'm a bit stuck with my homework in a subject called "Non-parametric Statistics". The task is related to Kruskal-Wallis test. The task is as follows: Let's look at the comparison of 3 independent ...
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A question about the change in value of multiple correlation coefficient on multiplying each value with a variable quantity

Question: I know the formula of multiple correlation coefficient is; ( |R| is the correlation matrix and R11 is the cofactor of the (1,1)th element of R. But I really cannot figure out, how to deal ...
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Matrix Approach to Linear Regression Model

How do we interpret a data matrix, $X$ which does not have $1s$ as the first column? Does it refer to No Intercept Form? Could it also be interpreted as the mean deviated form? I understand that for ...
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The probability distribution of waiting time until two exponentially distributed events with different parameters both occur

I am working on a problem related to the waiting time until a parking garage is empty. We are given that the cars independently spend an exponential distributed time in the parking garage, with ...
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To find the covariance given the joint probability density function.

Question: I was solving some question papers and got stuck in this problem. My problem: I know how to find "marginal probabilities" from a joint probability density function and also know how to ...
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Finding joint probability distributions from marginal distributions

Question: I was solving test papers where I found this one. My doubt: I know to work with conditional probabilities and Jaccobian Transformation and part A and B can be done applying the above..But ...
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Step-by-step tutorials on Bayesian Networks

I'm trying to study Bayesian Networks (BN), but during classes [1] we covered just some theory and no exercises were given. Therefore I'm looking for step-by-step tutorials or solved exercises for BN ...
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Multiple regression - Coefficients testing

I have a multiple regression model $Y=12.45+0.072X_1-0.15X_2+0.03X_3+0.17X_4$ with $R^2=0.972$ A second regression model is given as follows $Y=13.77+0.072X_1$ with $R^2=0.855$ The number of the ...
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Is it possible for a Bayes estimator to be independent of the sample?

I am trying to derive the Bayes estimator. Without getting into the nuts and bolts of the question, basically I have an indicator loss function of the form $$L(\delta , \theta) = \mathbb{1}\{A\}$$ ...
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Probability of sum of sequences of integers

Let K be a positive integer.Suppose that the integers 1,2,3,...,3k+1are written down in random order.What is the probability that at no time during this process, the sum of the integers that have been ...
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MASS{lda} plot in R [closed]

I'm reading the Introduction to statistical learning with R currently, but I blocked through a Lab about Discriminant analysis. So the thing is that we trying to fit a linear discriminant analysis ...
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Pearson differential equation distribution: gamma distribution derivation

How do I do 30a? It becomes extremely complicated if I solve the diff eq. with all the constants involved...
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What are good online course/s for learning optimization from beginning to advanced (linear, convex, integer, geometric, nonlinear, ..etc)?

I need some online course or group of courses, preferably videos, that allow me to understand optimization from the beginning. Give me a solid base knowledge (what is linear programing, what is convex,...
How to find joint distribution of $\min(U_0,U_1)$ and $\min(U_1,U_2)$ where $(U_0,U_1,U_2)$ are i.i.d Uniform?
I have this homework question where there are 3 random variables $(U_0,U_1,U_2)$ which are independent and uniform in the interval $[-1,1]$. I have two other random variables $(X,Y)$ defined as ...