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

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0answers
16 views

Convergence in distribution of the sum of two RVs

Let $X_n$, $Y_n$ and $Z_n$ be RVs such that $Z_n = X_n + Y_n$. Assume that $X_n$, $Y_n$ have joint distribution $F_n\left(x, y\right)$ and $X_n$ has a distribution function $F_n\left(x\right)$. Let ...
0
votes
1answer
50 views

Find a posterior distribution [on hold]

I came across this task that I have no idea how to solve, because I'm not very good at statistics, so I was wondering if someone could help me understand it. 7 scientists with very different ...
0
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0answers
8 views

Minitab: Variance/standard deviation calculator problem [on hold]

I have a small problem with the calculator in Minitab. The question is shown in the picture, and the highlighted is the portion that I am having problems with. Now, this is how it looks when I ...
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0answers
14 views

Conceptual Question On the application of Radial basis function in a paper

I am struggling with the concepts of using Radial basis function using radial basis neural network function in the application of modeling a PRBS signal sequence generated from a non-linear system. ...
1
vote
0answers
29 views

Probability of 10 (somewhat) consecutive events

My question to you: can you please tell me if I am doing things correctly or I am off base? Thanks! Objective: to determine the probability of 10 independent people having a one base pair mutation ...
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1answer
35 views

Statistical Significance

Our teacher told us If a test is rejected at 1% level of significance , then it will be rejected at 5% , 10% level of significance . I don't understand how does the rejection at 1% level of ...
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2answers
51 views

Reference request for beginner in SAS

I am interested to start learning to use SAS, I have used R for some time but for me SAS is a novelty. I do not seek any material in particular, since I'm now beginning to take the first steps with ...
2
votes
1answer
34 views

Regression without intercept: deriving $\hat{\beta}_1$ in least squares (no matrices)

In An Introduction to Statistical Learning (James et al.), in section 3.7 exercise 5, it states that the formula for $\hat{\beta}_1$ assuming linear regression without an intercept is $$\hat{\beta}_1 ...
1
vote
3answers
92 views

explanation of MCMC and bayesian estimation [on hold]

I have some questions about bayesian methods. First of all I have a set of iid observations, calling $y_1,\ldots,y_n$ that come from a certain distribution $f$ with unknown parameters(for example ...
9
votes
4answers
867 views

Why does the variance of the Random walk increase?

The random walk that is defined as $Y_{t} = Y_{t-1} + e_t$, where $e_t$ is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term. You can prove that ...
1
vote
0answers
35 views

Expected time in exponential distribution?

I'm using the exponential distribution to calculate a probability of an event to occur. $\lambda = 0.007$ failures/year. I am to calculate an expected time between 2 failures. My approach was to ...
1
vote
0answers
56 views

Mathematics / Statistics [on hold]

Today I was thinking how I'm bad at making statements, I know who does statistical cares more about the practical part, but knowing how to do demonstrations in the theoretical part is important? I ...
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0answers
15 views

Covariance of ARMA (2,1)

I am preparing for an exam and need help. Consider the following estimated ARMA(2,1) model, y(t) = 0,05 + 0,83y(t-1) + 0,13y(t-2)- 0,15e(t-1) + e(t): Given the unconditional variance and 1st order ...
0
votes
0answers
25 views

Figuring out which test to use

It's been a while since I've taken a stat's class and I came across a problem I need to solve. I was hoping someone could point me in the right direction. I know a question similar to this has ...
1
vote
1answer
23 views

Minitab question about binomial probabilities [closed]

What I have tried: My first instinct was to go to Calc>Binomial distributions> Binomial to get the graph of it. 2 questions: What does the question mean it needs values less than 21? Should ...
1
vote
1answer
42 views

Minimum-variance unbiased linear estimator

Suppose that it is known that the mean of RV $X_i$ is $\mu_i\theta$, (i = 1, 2,..., n), where $\mu_i$ are known constants, whereas $\theta$ is unknown. Let $\Sigma$ be the variance matrix of the ...
4
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2answers
163 views

Curse of dimensionality: kNN classifier

I am reading Kevin Murphy's book: Machine Learning-A probabilistic Perspective. In the first chapter the author is explaining the curse of dimensionality and there is a part which i do not understand. ...
1
vote
0answers
17 views

Dirichlet predictive distribution

I need to derive a posterior predictive density for observation T+1 given that the posterior distribution of $(x_{1}, x_{2}, 1-x_{1}-x_{2})$ is a Dirichlet distribution with parameter $(\alpha_{1}, ...
1
vote
0answers
48 views

Does central limit theorem (CLT) hold for non-integer values of $n$? [closed]

Search “not an integer” in http://www.math.uah.edu/stat/sample/CLT.html and you would find 2 occurrences of the author stating that CLT is valid even if $n$ is not an integer. If $X$ is assumed to ...
1
vote
0answers
72 views

Karlin-Rubin theorem and exponential family

Let $X_1,...X_n$ a random sample of $X$ with density $$f(x;\alpha,\beta)=\frac{\alpha}{x^{\alpha+1}}\beta^\alpha I_{[\beta,\infty]}(x)\space\alpha>0,\beta>0$$ with $\beta$ known. Find ...
0
votes
1answer
21 views

Order Statistics Conditional Distribution of Affiliated System

We have a system with $M (M\ge 2)$ random variables. The M variables are related as follows. For each i, 1 to M, $X_i = I_i+Z$, where $I_i$, Z are independent uniform random variables. What is the ...
3
votes
1answer
48 views

$E_{\theta_1}[\ell(\theta_2;X)] $

I am faced with the following in my "Statistical inference book" $E_{\theta_1}[\ell(\theta_2;X)] $ where $\ell(\theta_2;X)$ (loglikelihood) is $\log [P(\theta_2;X)]$, X is a random variable. What ...
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3answers
44 views

Exactly The Same Autocovariance Function of Two Time Series

A MA(2) process : $$X_t=W_t+\frac{5}{2}W_{t-1}-\frac{3}{2}W_{t-2}$$ where $\{W_t\}\sim WN(0,1)$ And another MA(2) process : $$X_t=W_t-\frac{1}{6}W_{t-1}-\frac{1}{6}W_{t-2}$$ where $\{W_t\}\sim ...
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0answers
21 views

3 correlated questions: Find the roots of an equation, find the inverse of a function and find the c.d.f. of a function of a random variable

I have 3 correlated questions: Find the roots of an equation, find the inverse of a function and find the c.d.f. of a function of a random variable. The questions are in the picture. Sorry for the bad ...
3
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1answer
72 views

Ways to find a UMP test

I'm studying for my final exams and the subject of proof will basically test hypotheses, I will try to summarize here my doubts. For found the UMP test the ways are 1) Use Neyman–Pearson lemma ...
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0answers
41 views

Calculating different Sample Errors [on hold]

A university plans to do a survey of the number of hours students spend studying each week to determine the average study time per student. It knows from previous surveys that the variability of study ...
2
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0answers
31 views

parametric bootstrap on regression

I keep trying to perform parametric bootstrap on simple regression analysis to grasp the concept. The internet is full of tutorials on non-parametric one, but I found no explanation or steps ...
1
vote
1answer
93 views

Optimization of a Convex Function involving Standard Normal CDF and PDF

Could someone provide closed form solutions, if any, and steps to get there for the following optimization problem? Please note this function has been shown to be a convex function and hence a minimum ...
8
votes
1answer
111 views

Convexity of Function of PDF and CDF of Standard Normal Random Variable

Please provide proof that $Q\left(x\right)=x^{2}+x\frac{\phi\left(x\right)}{\Phi\left(x\right)}$ is convex $\forall x>0 $. Here, $\phi$ and $\mathbf{\Phi}$ are the standard normal PDF and CDF, ...
4
votes
1answer
179 views

Conditional Expected Value of Product of Normal and Log Normal Distribution

EDIT: SIMPLIFIED EXPRESSION AND OTHER RELATED LINKS INCLUDED NOW Could someone please provide the answer and steps to solve this expression? \begin{eqnarray*} & & ...
2
votes
1answer
59 views

Copula density function

In the equation $h_t(x,y|...) = ...$, can anyone explain me why the first derivatives of the marginal distributions are included? $H_t$ is a distribution function and $h_t$ its density function. ...
0
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1answer
34 views

Poisson goodness-of-fit of small sample

Please note that I have no background in statistics - this is for personal interest. The post is inspired by a question at work. We were given data by another department asserting that for a ...
2
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1answer
53 views

Calculating probability for a continuous time markov chain

I can do question 1-3 no problem however I cant follow the steps to get the answer to part 4. Can anyone here explain the steps I need to go through in more detail?
2
votes
1answer
85 views

MCEM algorithm in normal distribution

Consider $z_1,\ldots,z_n$ as a sample of observations of $Z$ and $y_1,\ldots,y_n$ the missing data, where $Z\sim N(\mu,\sigma^2+1)$ and $Y\sim N(0,1)$. i)Find the expression of ...
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0answers
21 views

EM algorithm to impute missing value for one variable

This is from Robert Hogg's Introduction to Mathematical Statistics 6th, exercise 6.6.5. p366, It says, Suppose $X_1$, $X_2$, $X_{n1}$, are a random sample from a $N(\theta,1)$ distribution. Suppose ...
4
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2answers
56 views

Bayesian Network Problem: What is P(A=T, B=T, C=F, D=F)?

Suppose you have these probabilities in a bayesian network. What is P(A=T, B=T, C=F, D=F)? I attempted to answer this by saying that P(A,B,C,D) = P(A) P(B|A) P(C|A,B) P(D|A,B,C), according to the ...
1
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0answers
18 views

Multiple Regression - Calculate Elasticity of demand

If I assume that all of my regression coefficients are statistically significant then how to calculate the point own price elasticity of demand for given price=8, Advertise=10, Income = 50? ...
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0answers
15 views

Generalised Bayes minimax estimators

How do you prove that generalised minimax Bayes estimators are more numerical stable than the relative least squares estimators
2
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1answer
39 views

Neyman-Pearson Lemma and hypothesis-testing

Consider testing $H_0:\theta=\theta_0$ vs $H_1:\theta=\theta_1$, where the pdf or pmf corresponding to $\theta_i$ is $f(x|\theta_i)$, $i=0,1$ using a test with rejection region R that satisfies ...
1
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0answers
39 views

regression controversies

How can I test the relationship between my independent variable (in my case Price-Earnings ratio) and dependant variable (value of market deals), if I have a wide range of values of deals (400 deals ...
1
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0answers
27 views

plot LDA fit using R function plot()

I am doing the lab section: classifying the stock data using LDA in the book "Introduction to Statistical Learning with Applications in R", here is the lab video. Basically, this lab uses LDA to ...
2
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1answer
38 views

Likelihood ratio for normal distribution with known variance

Let $X_1,...,X_n$ random sample of $X$~$N(\mu,\sigma^2)$ with known $\sigma^2$.Take $a=.05$ find the expression for power function of the likelihood-ratio test $$H_0:\mu\leq 0\space vs\space ...
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0answers
16 views

Penalized quasi-likelihood

Can anybody explain me why the function glmmPQL(.) in R behaves in different ways, depending on the number of ...
0
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0answers
28 views

Contingency table model

Calculate the two regression coefficients and hence obtain the two regression lines from the following data I can find the two regression lines by using the equation y=b0 + b1x for ungrouped data. ...
4
votes
1answer
84 views

Using Poisson distribution to evaluate summations

I'm interested in how to use a Poisson distribution to evaluate $\sum\limits_{x=0}^\infty \frac{(x^2-x+1)(2^x)}{x!}$ I see that this is similar to the general pmf form of $\frac{2^{x}}{x!}$. My ...
2
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1answer
49 views

Likelihood-ratio test

I was studying on this subject and I got some questions. Lets take the test $$H_0:\theta\in\Theta_0 \space vs\space H_1:\theta\in\Theta_0^c$$ where $\Theta$ is the parametric space and ...
0
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0answers
27 views

Statistical Independence of Continuous variables

I recently had a quiz where I had to find out whether two variables were dependent or independent. I know that given $f(x,y)$ if $h(x)*g(y) = f(x,y)$ then they are independent, else dependent. I am ...
0
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0answers
15 views

using mgfs to find limiting distribution

Can someone help me out with proving that the limiting distribution of a negative binomial (k,p) distributed variable is poisson if we let k -> infinity and p->1. I am just learning about limiting ...
2
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1answer
44 views

Relationship between VC dimension and degrees of freedom

I'm studying machine learning and I feel there is a strong relationship between the concept of VC dimension and the more classical (statistical) concept of degrees of freedom. Can anyone explain such ...
1
vote
1answer
41 views

Maximum Likelihood, normal distribution

Let $Z$~$N(\mu,\sigma^2+1)$, find the maximum likelihood estimator for $\mu$ and $\sigma^2$. I did but I want to check that this right actually ...