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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.

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0answers
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How to carry out a Likert scale analysis?

Context: My research aims to assess whether parents who have been involved in a relationship with a social worker are at higher risk of child abuse/neglect. I am trying to establish whether there ...
3
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0answers
89 views

The boundary proprerty of conjugate exponential family

Consider a conjugate prior in the k-parameter canonical exponential family: $$p(w|n_0,y_0)=c(n_0,y_0) \exp(n_0(y_0 w'-b(w))) \, ,$$ where $n_0>0, y_0 \in Y$ is the pseudo observation vector, and $...
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1answer
236 views

Expected number of shipments and its standard deviation

Recent history suggests that one supplier fails to meet this new specification 20% of the time. Assume that the next 15 batches of this alloy are a random sample. How can I find the expected number ...
10
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1answer
15k views

Coverage probabilities of the basic bootstrap confidence Interval

I have the following question for a course I'm working on: Conduct a Monte Carlo study to estimate the coverage probabilities of the standard normal bootstrap confidence interval and the basic ...
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votes
1answer
14k views

How do I deduce the SD from regression and ANOVA tables?

This is a Minitab printout. I want to find the value of A5, or S. I think S is supposed to be the sample standard deviation, but I don't know how to calculate it. Any tips on how I should go about ...
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1answer
9k views

Difference between sampling distribution and data distribution

I went to a stats course refresher last week and the instructor talked about data distribution and sampling distribution. I am just practicing with the exercises shown in class. Based on my dataset ...
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2answers
286 views

Derivation of bayesian confidence interval

How do you derive the expression for the $100(1-\alpha)$% bayesian confidence interval when working with the uniform distribution in the interval $[-\theta,\theta]$?
5
votes
1answer
14k views

Calculating the mean using regression data

I have some data to analyze where $y$ is dependent of $x$ - a linear regression was used. It's a question from an exam, so I think it should be solvable. The regression was used to estimate the mean ...
3
votes
1answer
103 views

Given pdf of $I$ and $R$ (both $I$ and $R$ are independent RV's), how to find pdf of $W =I^2\cdot R$?

The title defines the question. May be the concept would do...like how to go about it? Thanks.
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2answers
4k views

Monte Carlo experiment to estimate coverage probability

I'm working on a problem as follows for a course that I'm auditing: Suppose a 95% symmetric t-interval is applied to estimate a mean, but the sample data are non-normal. Then the probability that ...
5
votes
3answers
1k views

Looking for stats/probability practice problems with data and solutions

I am looking for a self-study site on the web that will allow me to verify my understanding of some basic probability and stats concepts and operations. What I would like is a site with data and ...
4
votes
1answer
4k views

How to find percentiles of a Normal distribution?

A lecturer wishes to "grade on the curve". The students' marks seem to be normally distributed with mean 70 and standard deviation 8. If the lecturer wants to give 20% A's, what should be the ...
3
votes
1answer
937 views

Dual problem for L2 support vector machine

Here is the dual problem for L2 support vector machine: $$\max_{\alpha\in\mathbb{R}^{n}} 2\alpha^{T}y-\alpha^{T}\left(K+n\lambda Id_{\mathbb{R}^{n}}\right)\alpha$$ $$\forall i\in\left\{ 1,\ldots,n\...
2
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1answer
620 views

Linear discriminant analysis and the “kernel trick”?

This is problem 12.10 in "The Elements of Statistical Learning": Suppose you wish to carry out a linear discriminant analysis (two classes) using a vector of transformations of the input ...
4
votes
1answer
1k views

Gaussian kernel estimator as Nadaraya-Watson estimator?

I'm working on a problem from "The Elements of Statistical Learning" (prob. 6.8): Suppose that for continuous response $Y$ and predictor $X$, we model the joint density of $X, Y$ using a ...
2
votes
1answer
459 views

Algebraic definition of a residual from a regression

Can anyone give some advice on how to start proving this algebraically? Define the residual from a regression (one independent variable) algebraically and show that: the mean of the residuals is ...
4
votes
1answer
642 views

Sampling from a fixed population

Here's a real basic question. I'm trying to teach myself a bit of stats with Verzani's Using R for Introductory Statistics. In question 5.13 he asks: A sample of 100 people is drawn from a population ...
1
vote
2answers
884 views

Seeing if estimators are unbiased

I have the pdf $$f(y ; \theta) = \frac{1}{\theta} \exp( \frac{-y}{\theta}), \ y > 0$$ and I'm supposed to determine if the following two estimators are unbiased or not: $ \hat \theta = nY_{min} $...
2
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1answer
1k views

Normal distribution and weight of babies problem

X is the weight of a baby when born (in gram). If the distribution of X is N(3315, 575) and Y is the number of babies with weight lower than 2719 in a random sample of 25, then P[Y≤4] is about...? I'...
6
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2answers
2k views

How do you solve a Poisson process problem

During an article revision the authors found, in average, 1.6 errors by page. Assuming the errors happen randomly following a Poisson process, what is the probability of finding 5 errors in 3 ...
7
votes
1answer
410 views

Minimum tickets required for specified probability of winning lottery

In a lottery, 1/10 of the 50 000 000 tickets give a prize. What is the minimum amount of tickets one should buy to have at least a 50% chance to win? Would be very glad if you could explain your ...
1
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1answer
1k views

Fitting normal distribution to given quantiles

Hey everyone, thanks for taking the time to look at this question. This is pretty simple, and I understand statistics quite well, but I think I'm not wrapping my head around the words, it seems to me ...
9
votes
1answer
1k views

Least angle regression keeps the correlations monotonically decreasing and tied?

I'm trying to solve a problem for least angle regression (LAR). This is a problem 3.23 on page 97 of Hastie et al., Elements of Statistical Learning, 2nd. ed. (5th printing). Consider a regression ...
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2answers
4k views

Expected number of runs of length n in coin toss

I'm writing a program for an assignment for my Probability and Statistics course. This program performs several millions of simulated coin tosses, and then analyses various properties of the generated ...
3
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1answer
253 views

Probability of getting between

...2 to 5 questions answered correctly, out of 20 of them? Each question has 5 choices. Probability of getting one right is 1/5. Probability of getting exactly 1 right is ${20 \choose 1} p^1 q^{19}$, ...
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2answers
1k views

Maximum likelihood and sufficient statistics

fT(t;B,C) = exp(-t/C)-exp(-t/B) / C-B where our mean is C+B and t>0. so far i have found my log likelihood functions and differentiated them as follows: dl/dB = sum[t*exp(t/C) / (B^2(exp(t/c)-exp(t/...
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votes
2answers
13k views

How to use Confidence Intervals to find the true mean within a percentage

I'm working through a practice problem for my Stats homework. We're using Confidence Intervals to find a range that the true mean lies within. I'm having trouble understanding how to find the required ...
7
votes
3answers
10k views

Proving that the squares of normal rv's is Chi-square distributed

I start with three independent random variables, $X_1, X_2, X_3$. They are each normally distributed with: $$X_i \sim N(\mu_i, \sigma^2), i = 1, 2, 3.$$ I then have three transformations, $$\...
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votes
3answers
483 views

What logistic regression is best to use?

My project is about whether early language scores (on a reading task) can predict later scores on a social attribution task. I have to conduct a logistic regression for my project but I am stuck on ...
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1answer
138 views

Probability and limits

I've been having some trouble with this story problem. Any help you could give me would be really appreciated. A store manager monitors the store's temperature by taking 4 independent temperature ...
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3answers
2k views

Normal distribution probability

The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with stocks having a mean of 15% and a ...
2
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2answers
2k views

Correction due to rounding error

The height for 1000 students is approximately normal with a mean 174.5cm and a standard deviation of 6.9cm. If 200 random samples of size 25 are chosen from this population and the values of the mean ...
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2answers
2k views

Minimization of a function by Metropolis-Hastings algorithms

When minimizing a function by general Metropolis-Hastings algorithms, the function is viewed as an unnormalized density of some distribution. (1) As density functions are required to be nonnegative, ...
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votes
3answers
10k views

Calculating the error of Bayes classifier analytically

If two classes $w_1$ and $w_2$ have normal distribution with known parameters ($M_1$, $M_2$ as their means and $\Sigma_1$,$\Sigma_2$ are their covariances) how we can calculate error of the Bayes ...
6
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3answers
4k views

VC dimension of SVM with polynomial kernel in $\mathbb{R^{2}}$

What is the VC dimension of SVM with the polynomial kernel $k(x,x')=(1+<x,x'>_{\mathbb{R^{2}}})^{2}$ for binary classification in $\mathbb{R^{2}}$? It would be equal or more than v iff ...
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5answers
6k views

Better Classification of default in logistic regression

Full Disclosure: This is homework. I've included a link to the dataset ( http://www.bertelsen.ca/R/logistic-regression.sav ) My goal is to maximize the prediction of loan defaulters in this data set. ...
4
votes
1answer
5k views

Internal reliability for an ordinal scale

My teacher is asking whether it is possible to look at the Cronbachs's alpha when looking at the internal reliability of an ordinal scale. She thinks, because you use the mean of it, it is not ...
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2answers
21k views

Interpreting the step output in R

In R, the step command is supposedly intended to help you select the input variables to your model, right? The following comes from ...
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2answers
30k views

Interpreting the drop1 output in R

In R, the drop1command outputs something neat. These two commands should get you some output: example(step)#-> swiss ...
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2answers
2k views

Comparison of two values in a statistically sound manner

For a university paper, I have to compare whether two program versions are statistically significantly different. The comparison in terms of runtime performance is straightforward -- I determine ...
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4answers
58k views

How to compute the steady state gain from the transfer function of a discrete time system?

Having the Transfer Function of a discrete system as such: $$H(z) = \frac{0.8}{z(z-0.8)}$$ I am asked to find the Steady State Gain of the system. I have the solution and it simply states: Steady ...
4
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1answer
555 views

Factorization of a joint density over a directed graph

Let $G = (V,E)$ be a directed acyclic graph. Let $i \rightarrow j$ be an edge such that the parents of $j$ are exactly: the parents of $i$, and $i$. Let $L\left(G \right)$ be the set defined by ...
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1answer
4k views

Calculating quantiles for chi squared distribution

For chi squared distribution, how would I find quantiles for the following three cases: A) $P(X^2> X^2_{\alpha})=0.01$ when $v = 21$ B) $P(X^2 < X^2_{\alpha})=0.95$ when $v =6$ C) $P(X^2_{\...
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4answers
2k views

Small sample linear regression: Where to start

FULL DISCLOSURE: This is homework. I have been provided with a small data set (n=21) the data are messy, looking at it in a scatterplot matrix provides me with little to no insight. I've been ...
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1answer
2k views

How to test for parallelism for two linear models?

I'm taking a graduate course in regression analysis and I'm suck on a particular homework question that should be very simple to me! I have the following model: ...
8
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1answer
13k views

Regression Proof that the point of averages (x,y) lies on the estimated regression line

How do you show that the point of averages (x,y) lies on the estimated regression line?
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1answer
2k views

Statistics Proof that $E[(X-Y)^2] = 0$

If X and Y are standardized variables and are perfectly positively correlated with respect to each other, how can i prove that $E[(X-Y)^2] = 0$?
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1answer
2k views

Finding marginal densities of $f (x,y) = c \sqrt{1 - x^2 - y^2}, x^2 + y^2 \leq 1$

As the title says, I'm looking for the marginal densities of $$f (x,y) = c \sqrt{1 - x^2 - y^2}, x^2 + y^2 \leq 1.$$ So far I have found $c$ to be $\frac{3}{2 \pi}$. I figured that out through ...
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2answers
329 views

Log graph question

So let's say you have a distribution where X is the 16% quantile. Then you take the log of all the values of the distribution. Would log(X) still be the 16% quantile in the log distribution?
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7answers
3k views

How should one approch Project Euler problem 213 (“Flea Circus”)?

I would like to solve Project Euler 213 but don't know where to start because I'm a layperson in the field of Statistics, notice that an accurate answer is required so the Monte Carlo method won't ...