Questions tagged [statistical-inference]
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The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.
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Precision and sample size
Say I measured the length of one object 100 times and I wanted to compare how the sample size affects my precision. If all 100 data points are included, the precision of my measurements will most ... statistics statistical-inference- 1
Conditional expectation on squared sum of independent random variables
Given $X$ and $Y$ independent random variables of means $0$ and variance equal to $\sigma^2$, and $Z = X + Y$, find the conditional expectation $E[Z^2|X = x]$ for any value $x$ where the conditional ... probability statistics statistical-inference conditional-expectation- 82
Error types and statistical tests
Given the following statistical test: $$H_0:\mu=12\mathrm{\ min}$$ $$H_1:\mu<12\ \mathrm{min} $$ Determine the best test (critical value and sample size), if the probability of not detecting a ... probability statistical-inference hypothesis-testing- 1
Agreement on a Likert scale
I've conducted an experiment in the form of a Likert survey in which $15$ persons participated. They were each presented with $35$ questions and asked to pick an answer on a $5$-point Likert scale (... statistics statistical-inference- 535
find the complete statistic for Uniform($\theta,\theta+1$)
Assume $x_1x_2,\dots,x_n$ are i.i.d Uniform($\theta,\theta+1$), want to know if $x_{(n)}$, the order statistic, is a complete statistic. This appears in a course slides, but I don't know if the result ... statistics statistical-inference- 173
Confidence interval difference of proportions with bootstraping
I have this model: M1 <- glmmPQL(outcome~tratf,random=list(~1|id) ,ejemplo7 ,niter=50, family=binomial) summary(M1) I want to calculate the 95% confidence interval for the difference in proportions,... statistical-inference bootstrap-sampling- 21
Car rental time series forecasting
I have the time series of car rentals/demand in a location. The time axis is every hour for 3 months. The y-axis is number of car rentals/demand. I want to do prediction for future hours given this ... statistical-inference time-series- 238
Density function of Uniform sample mean [duplicate]
Let $X$ be a random variable that is uniformly distributed over the interval $[0,1]$. A simple random sample of size $2$ is taken from it, denoted by $X_1$ and $X_2$. Find the density function of the ... probability statistics statistical-inference uniform-distribution- 82
How to derive critical region of binomial distribution LRT
The question is as follows: Consider an iid sample $\{X_1, \cdots, X_5\}$ out of tossing a coin 5 times. Each $X_i$ takes 0 or 1 depending on whether $i$th toss is head or tail, respectively. Let $p$ ... statistics statistical-inference hypothesis-testing- 3
What are the difference between Causation Confounder and Collider in a Bayesian Network?
Intro I am currently doing self-study on Bayesian networks. I saw on some slides that there are different ways to model dependencies (See the linked screenshot). These ways are called causation, ... statistics statistical-inference independence bayesian bayesian-network- 3
Finding lower bound of maximum age through set of observations [closed]
In another planet, it is believed that humans live only upto some maximum age $A$, however they might die at any age lower than $A$ for any reason like disease. We are interested to pin down this ... statistics normal-distribution statistical-inference upper-lower-bounds data-analysis- 1
Expresses the rejection region by quantiles
I am solving a uniformly more powerful test problem and I find that the rejection region is: $$ C = \left\lbrace (x_1,\ldots,x_n): \sum_{i=1}^nln(1-X_i)>k^* \right\rbrace $$ where $k = \frac{ln(k\... probability statistics statistical-inference- 435
Estimating the parameter $\theta$ using method of moments
Let $(x_1=2, x_2=3,x_3=2, x_4=2 , x_5=2)$ be a random sample from a population with density function $f(x)=\left(\frac{1}{\theta}+1\right)x^{\frac{1}{\theta}-1} $ where $0<x<1$ and $0<\theta &... statistics statistical-inference parameter-estimation- 4,040
Confidence interval of predictor
Assume we have a random variable $Y\in N(0,\sigma_Y^2)$ and $Z\in N(0,\sigma^2_Z)$. For the random variable $Y$ and $Y+Z$, we have that the correlation is given by $$\rho=\frac{Cov(Y,Y+Z)}{\sqrt{\... statistics statistical-inference correlation confidence-interval- 1
Transformation of a mixture of bivariate Normal distributions to polar coordinates
The pdf of a mixture of normal distribution is $f_{X,Y}(x,y) = \pi N(\mathbf{\mu}_1, \Sigma_1) + (1-\pi) N(\mathbf{\mu}_2, \Sigma_2)$. Is it possible to transform this distribution to the polar ... probability statistics statistical-inference jacobian mobius-transformation- 433
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