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1answer
9 views

How to compare whether the coefficients of two independent variables statistically different from each other?

If I have two independent variables and they are dummy variable along with other independent variables and I run a linear probability model, I want to compare whether the coefficients of two dummy ...
1
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0answers
27 views

Bayesian mean square error

Given a i.i.d sample $X_{1},..,X_{n}$ of bernoulli random variables test 2 hypotheses $H_{0}:p=2/3$ and $H_{1}:p=1/3$. Bayesian prior is $\pi(2/3)=1/3$ and $\pi(1/3)=2/3$. Find the bayesian criterion ...
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0answers
12 views

White standard errors and Weighted Least Squares (WLS) [on hold]

Are there situations in which it would be useful to apply WLS and use White standard errors (from the transformed model) as well?
2
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0answers
31 views

Which observation has the largest variance of the residual?

a) For which of the following observations (obs1, obs2, obs3) is the variance of the residual the largest? Which observation has the highest leverage? And which one the smallest? Explain why. ...
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0answers
19 views

How to calculate false accept and reject rates in pattern recognition?

I am working on a vein pattern recognition project based on SURF algorithm and Euclidean distance. I have completed my program to find the maximum and minimum distance between vein features and find a ...
2
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1answer
45 views

Conditional Probability equal to zero

Let $X_1$ and $X_2$ be two independent Normal variables with mean $\theta$ and variance $1$. Let $S=X_1+X_2$ and consider the following conditional probability: $$P \left[ X_1 \leq x_1; X_2 \leq x_2 ...
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0answers
31 views

Proving that Markov Chain Monte Carlo converges

I actually asked the same question in http://math.stackexchange.com/ as well at http://math.stackexchange.com/questions/753105/proving-that-markov-chain-monte-carlo-converges but since the question is ...
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2answers
43 views

Finding a statistically different proportion

I have the following problem: given a proportion $p_1=\frac{X_1}{n}$, where $X_1$ is the number of succesful outcomes in $n$ tries ($X_1$ and $n$ are both > 100), I have to find the smallest ...
1
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1answer
41 views

How should you fit ANOVA and linear regression models, if the equal variance assumption is violated?

This is my topic for the paper I'm working on for an undergrad stats class. It's supposed to be 20 pages... and I'll be honest, I understand very little beyond the basics and am over my head. From ...
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0answers
22 views

Expected mean square of random effect in CRD model

Random effect in CRD model: \begin{align} y_{ij} &= \mu + \tau_{i} + \varepsilon_{ij} \\ \tau_{i} &\sim \mathcal N(0,\sigma_{\tau}^2) \\ \varepsilon_{ij} &\sim ...
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2answers
238 views

Expected sum of money

There is a little problem in the working on this one I have encountered recently. Here it goes: Starting off with \$100, when you toss a coin, if there is a tail, you will get \$10 and lose $10 if it ...
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0answers
54 views

What is the distribution of this ratio of quadratic forms?

I guess it's F-distribution but I don't know what the solving process it is
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0answers
21 views

Prove mutually independent

I tried it using some theorem...but I can't Can someone give a proof of this plase? I can't sleep because of it!
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0answers
17 views

Meaning of marginal prior distribution

I have a variable $\mu$ with distribution, given $\phi$ of $ \mu|\phi \sim N(\phi, \sigma^2)$, and the distribution of $\phi$ is $\phi \sim N(\nu, \tau^2)$. (Here, $\sigma^2,\nu$ and $\tau^2$ are ...
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0answers
33 views

T-test homework [closed]

Suppose a manufacturer claims that each family size bag of pretzels sold weighs 12 ounces on average with a standard deviation of 0.8 ounces. A consumer's group decides to test this claim. If a simple ...
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0answers
11 views

Choosing an appropriate proposal distribution for metropolis hastings

So far the only constraint I've found for sampling from some target distribution $\pi(x)$ is that the proposal distribution must include the support of $\pi(x)$. That's very vague. What makes a ...
2
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1answer
30 views

Representation of ARMA processes

Question Consider the following process: $$2y_t-3y_{t-1}+y_{t-2}=\epsilon_t-\theta\epsilon_{t-1}$$ What is the model for the process $w_t=\Delta y_t = y_t-y_{t-1}$? Attempt I have solved the ...
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1answer
30 views

Learning multivariate techniques to analyze the gut microbiome

I would like to start learning some of the basics regarding data processing and analysis of microbiome data using R. Can anyone recommend a tutorial on some of the core/basic approaches that also ...
0
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2answers
47 views

Expected value of multiplication of Identically distibuted random variables

i am trying to understand if the following statement is true: $$ E(XY)= E(X^2)=E(Y^2) $$ if $X$ and $Y$ are identically distributed but not necessarily independent r.v. This means that if the ...
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0answers
29 views

Marginal distribution of a function of order statistics

From the joint distribution of any two order statistics, say $Y_j$ and $Y_k$, $j<k$ I would like to derive the distribution of $Z=F(Y_k)-F(Y_j)$. The initial pdf is: $$f_{Y_j,Y_k} (y_j,y_k) ...
3
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0answers
71 views

covariance term in simple linear regression

I am trying to derive the expression for variance of $\hat{\beta_0}$ in simple linear regression. I substitute $\bar{y} - \hat{\beta_1} \bar{x}$ for $\hat \beta_0$ but in the intermediate steps the ...
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0answers
10 views

Homogeneity of Variance, 2 Way Completely Crossed Design

I am looking for some advice as to how I might handle having an unfavorable Levene's test outcome, that is to say a highly significant value. DOE Various containers with water were microwaved for ...
0
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1answer
73 views

How to get P-Value when t value is less than 1?

I am doing an assignment for class and I have hit a wall. I'm not sure what to do next. Using a sample with 12 discrete elements, I am trying to test a hypothesis that the population mean is 243 ...
0
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2answers
45 views

Function of random variable

If I have a random variable $X$ which has mean $\mu$ and variance $\sigma^2$, what is the approximate expression of $log(X)$ and $\sqrt{X}$? Do I assume normal approximation or use Taylor expansion?
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0answers
23 views

Assuming training data as set of target funtions

In this 10th slide of http://www.cs.cmu.edu/afs/cs.cmu.edu/project/theo-20/www/mlbook/ch6.pdf presentation The Training data set $D$ is assumed as the set of target function . Actually $D = ...
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0answers
23 views

Standard mean and deviation

A company supplies specialized high-tensile pins to a customer.It uses an automatic lathe to produce the pins.Due to factors such as vibration, temperature and wear and tear, the lengths of pins are ...
2
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1answer
40 views

showing a random variable has an exponential distribution

Let $X_{1},..,X_{n}$ be independent, each with a exp($\lambda$) distribution. Let $Z=min(X_{1},..X_n)$. Show that $n\lambda Z$ has an exp$(1)$ distribution. I calculate that $P(Z>z)=e^{-n\lambda ...
1
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1answer
45 views

Formulas for probabilities in Bayes theorem

In continuation to this question $p(h|D) = \frac{p(D|h)p(h)}{p(D)}$ $p(h) = $prior probability of hypothesis $h$ $p(D)$ = prior probability of training data $D$ $p(h|D)$ = probability of $h$ ...
3
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1answer
53 views

Simulate the distribution of the median

I have done part(a); now I need to do part(b): I want to simulate the distribution of the median $M$ using R. I don't know how to work it out. And for part(c), do I need to use R as well? This is ...
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0answers
16 views

Gamma Distribution MGF

I'm not sure how to find part a, what formula can be used to find this mgf?
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0answers
33 views

Random model selection and validity of significance tests

Suppose we have some data, $\{y_i, x_{1i}, \dots, x_{ki}\}_{i=1}^n$ and we want to build a linear model of the form $y_i = \beta_0 + \beta_{1'i}x_{1'i} + \dots + \beta_{k'i}x_{k'i} + \epsilon_i$, ...
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0answers
43 views

Poisson distribution help

In many cities, neighborhood Crime Watch groups are formed in an attempt to reduce the amount of criminal activity. Suppose one neighborhood that has experienced an average of 10 crimes per year ...
1
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1answer
76 views

Constructing one-ninth fraction of the $3^{5}$ design

I want to construct a $3^{5-2}$ design with $I=ABC$ and $I=CDE$ as generators. The complete defining relation for this design is: $I=ABC=CDE=ABC^{2}DE=ABD^{2}E^{2}$. This is a resolution III design ...
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3answers
161 views

What is a “strictly positive distribution”?

I am reading Judea Pearl's "Causality" (second edition 2009) and in section 1.1.5 Conditional Independence and Graphoids, he states: The following is a (partial) list of properties satisfied by ...
0
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1answer
59 views

construct the maximum likelihood estimator

Let $a_{1},a_{2},a_{3}$ be independent with a normal(0,1) distribution. Define $X_{1},X_{2},X_{3}$ by $X_{1}=a_{1}$, $X_{2}=\theta X_{1}+a_{2}$ and $X_{3}=\theta X_{2}+a_{3}$ Find the MLE for $\theta$ ...
1
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2answers
43 views

which model should I use in order to represent stock market price from theoretical perspective?

I am studying my lecture notes where I saw this: $Y_t=Y_{t-1} +u_t$ $Y_t=0.5* Y_{t-1} +u_t$ $y_t=0.8* u_{t-1}+u_t$ The first two models are AR(1) and the third one is an MA(1) model. In the ...
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1answer
52 views

Two easy probability tasks

I'm struggling with two exercises for which I do possess answers, but I have no idea why they would be like that. I haven't done any statistics in a long time (restarting studies). Question 1 Two ...
2
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1answer
37 views

The effect of ommission of relevant variable in the regression model on adjusted $R^2$

Let's say I have two regression models (I) $y_t=\beta_1+\beta_2 x_2+u_t$ (II) $y_t=\beta_1+\beta_2 x_2+\beta_3 x_3 + u_t$ How the omission of relevant variable (not irrelevant variable) affects ...
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0answers
33 views

Channel capacity

A binary channel is described with following conditional probabilities: $p(y_1|x_1)=1, \quad p(y_1|x_2)=p(y_2|x_2)=\frac{1}{2}$ Additionally, we know that "1" appears 13 times more ...
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0answers
16 views

the non-rejection region in level of significance approach eqaul to the area determined by upper and lower bounds in confidence interval approach

For $H_0: \hat \beta=\beta^*$ I want to prove that the non-rejection region in level of significance approach Will be eqaul to the area determined by upper and lower bounds in confidence interval ...
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0answers
11 views

How would you test for high order autocorrolation

The question is the following; And I determine the intervals If I Will do breusch-godfred test, I guess accourding to these interval, I can find high order correlation. But I dont know how to ...
0
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1answer
31 views

Probability on Z-score

I have a data of 30 values that represent returns on investment and which have a mean of 7 and standard deviation of 14. We are talking here about normal distribution. Now I am being required to do a ...
1
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1answer
52 views

PCA loadings and valid principal components

I am a beginner and in the process of understanding PCA. I came across the following question Suppose we have a data set where each data point represents a single student's scores on a math test, ...
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0answers
22 views

Method of Composition to sample from a t density

I got stuck with this, I will appreciate a lot any help. I need to make an R program in order to run this algorithm (in the photo below), with simulated data. The question is to use the method of ...
1
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1answer
49 views

Is the data normally or lognormally distributed?

I'm not sure how to give context to this question. We're to use Excel to analyze data and use log base 10 for each column of data that we analyze, which I'm not sure what they want here. Are they ...
0
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1answer
57 views

probability that a year has 53 mondays

We have the years from 2001, 2002, 2003,... to 2010. Say, a year is chosen at random from the listed years. What is the probability that the chosen year has 53 Mondays ?
3
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2answers
140 views

Differencing a time series

I am looking to find the ACF of a time series, but after it is differenced. $y_t = a_1y_{t-1} + \epsilon_t , \mid a_1 \mid < 1$ I understand that to find the ACF this process needs to be ...
0
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1answer
37 views

Which arma model is best one?

I am studying ARMA models. ARMA(25,25) or ARMA(1,1) which one better model? Why? I think that the reason is the ommission of irrelevant variable
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0answers
8 views

Comparison test in unit root

I am not clear how to compare all the tests in Unit Root. Which one is the most powerful among: ADF PP KPSS Elliott, Rothenberg & Stock Unit Root Test
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0answers
43 views

Testing if alcohol consumption and smoking are independent

The question asks to test if smoking status and level of alcohol consumption are independent using the usual five-step procure at alpha $=0.05$: I am having trouble finding expected values. As the ...