# Tagged Questions

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

67 views

23 views

46 views

41 views

19 views

### using the Cramer-Rao bound to find the approximate variance of a bernoulli trial

Given you have an independent random sample $X_1, X_2,..., X_n$ of a Bernoulli random variable with parameter $p$, estimate the variance of the maximum likelihood estimator of $p$ using the Cramer-Rao ...
23 views

### What is the standard deviation of the sample distribution for the sample standard deviation?

I know that for the sample distribution for the sample mean given a large sample or a normal underlying distribution, the mean of the sample distribution is the population mean of the underlying ...
52 views

### rigorous statistics book recommendations

I am learning statistical inference by myself, I have skim through a few books like Casella Hoggs and I find it omitted lots of details, for example, they didn't introduce the conditional expectation, ...
18 views

### What statistical tests should I perform to determine significance in differences between control, treatment, and sham groups?

Say I have 3 groups of scores: one control, one treatment, and one sham. I want to determine whether there is a significant increase (or decrease) in the mean scores with the treatment compared to the ...
19 views

### Hypothesis testing using proportions

Suppose that you interview 100 exiting voters about who they voted for governor. Of the 100 voters, 55 reported that they voted for the Democratic candidate. Is there sufficient evidence to suggest ...
23 views

### Hypothesis testing and the size of critical region

I'm studying stats in order to obtain a certificate and I'm struggling with this question. I've searched a lot and I really didn't understand how to procede in this question. I even don't know how to ...
86 views

### How to solve an integratation involved an unknown function?

Can anyone have any suggestions how to solve this equation for $w_i$, that is, what is the solution of $w_i$? $$\int_0^\infty e^{\Phi^{-1}(w_i)ε_i}P(r_i│ε_i )f(ε_i )dε_i=δ$$ Where, $f(ε_i)$ is the ...
31 views

### How can I determine the best relationship for 3 variables, given several data points?

What is the best way to determine the relationship for three apparently related variables? The relationship does not appear to be linear, and may follow a combination of non-linear functions. I have ...
12 views

### Bayesian Inferences: Finding Posterior HPD Interval

I am currently working with Beta-Bernoulli and Beta-Binomial models. I have been searching around for the specific steps in obtaining the Posterior HPD intervals for both. Does anyone know how to find ...
43 views

24 views

### If the conditional expectation of the random variable does follow a linear function, can we show the probability a particular data set happens?

Suppose that $\mathbb{E}[Y\mid X=x]=\beta_0+\beta_1x$ where $X, Y$ are random varibles. Given a set of observations consisting pairs of $X,Y$, is it possible to attach it as probabiltiy density ...
16 views

### Moment generating function of quadruple-form of Gaussian RVs

Let $X \sim N(0, I_d)$ be a $d$-dimensional Gaussian random variable. Let $\beta_1$ and $\beta_2$ be two $d$-dimensional vectors. I would like to compute expectation \begin{align} \mathbb{E}\Bigl \{ \...
22 views

### Using the normal approximation, what is the $z$-value of a sample difference of $\hat p_1−\hat p_2=−0.18$? [closed]

A few concepts from my textbook that I do not understand: If the Random, Normal, and Independent conditions are met, then is it true that $\hat p_1+2\hat p_2$ is approximately normally ...
18 views

### how to determine the expected value of the first element of an ordered statistic

let $X$ be a random variable with density $$f_x(x) = e^{\alpha-x} \: x>a$$ (a) what is the maximum likelihood estimator for alpha (b) make the estimator in (a) unbiased, and evaluate its ...
68 views

### Estimate of Proportion

An airline is interested in determining the proportion of its customers who are flying for reasons of business. If they want to be 90 percent certain that their estimate will be correct to within two ...
66 views

### Obtain a $(1-\alpha) 100$% confidence interval for $\theta$ using the moment estimator

Suppose $x_1,..x_n$ is a random sample from a distribution with probability density $f(x|\theta )=\theta x^{\theta -1} 0<x<1 \ and \ \theta >0.$ Find the moment estimator of $\theta$ and ...
20 views

### One-sample t tests for sample mean with outliers

In carrying out a one-sample t test for a sample mean, how should outliers be dealt with? For example, for the data ${110, 110, 110, 118, 122, 150}$ in a sample size of 6, evidently $150$ is an ...
9 views

### How to find the effects of the parameters with the Latin Hypercube Simulation?

We are working with an epidemic model where we have 21 parameters which affect the $R_{0}$-value. We want to study the effect of those parameters on the $R_{0}$-value with the Latin Hypercube ...
31 views

### Why this equation holds, using Bayes formula?

My mysterious equation is: $$p(x|\chi)=\int_{\theta\in\Theta}p(x|\theta)p(\theta|\chi)d\theta$$ where $\chi$ is some samples drawn from sample space parameterized by $\theta\in\Theta$. Follows the ...
38 views

### Correctly calculating the bias of an estimator

I'm currently learning about method of moments and maximum-likelihood estimators and have confused myself with this issue: First, let me estimate the parameter $\lambda$ from the exponential ...
28 views

### Confidence intervals and significance tests

A sample is used both to construct a 95% confidence interval for a population proportion p and to run a significance test with null hypothesis $H_0:P=0.07$ and significance level $\alpha=0.05$. Is it ...
Let $X_1, ...,X_n$ be a random sample from the following pdf: $f(x) = e^{-(x-\theta)} \exp(e^{-(x-\theta)}), -\infty<\theta<\infty$ a. Define $W=\log(\sum_{i=1}^{n}e^{-X_i})$.Shoe that \$\bar{...