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

learn more… | top users | synonyms

0
votes
0answers
7 views

Inferring Probabilities from relative frequencies

I have an question concerning the converse strong law of large numbers By the Converse Strong Law of large numbers, i mean the general principle (2) which is the converse of the standard strong law ...
0
votes
0answers
11 views

Random Variables and Statistic

I'm studying Statistical Inference by Casella and I'm confused with the definitions of random variable & statistic. So let we have the probability space $(\Omega, F, P)$ where $\Omega$ is the ...
0
votes
0answers
22 views

Deriving a formula for a confidence interval

Derive a formula for a $(1-\alpha)100\%$ C.I. for $\mu_x -\mu_y $ for data that has the following properties: A random sample $X_1,X_2...X_n \ are \ i.i.d ~N(\mu_x, \sigma^2 ) $ Another random ] ...
2
votes
0answers
27 views

How sample size affects confidence interval.

Suppose the weight of n primary one students has sample mean of 20KG. If n = 40, a certain percentage of confidence interval for the population mean is (15.5,24.5). Find the confidence interval if we ...
0
votes
0answers
16 views

F-test and T-test produce the same results

I am modelling a stochastic process by two different methodologies and I expect the results of each to be normally distributed with identical means and stdevs. To test that the distributions after ...
0
votes
0answers
15 views

Why is the expectation of the score function 0? [on hold]

Intuitively, why is the expectation of the score function 0?
1
vote
1answer
22 views

Interval estimate to infer the population mean with a 95% confidence level

An industrial designer wants to determine the average time it takes for an adult to assemble a toy. 24 people were randomly chosen to assemble the toy and the time taken (in minutes) were as follows: ...
0
votes
0answers
10 views

Forecasting disputed transaction frequencies

Problem I would like to forecast credit card chargeback/dispute frequencies using historical dispute data I have recorded over time. The data I currently store includes: Disputed transaction date ...
4
votes
0answers
11 views

Intuitive explanation of requirement for achieving the Cramer Rao Lower Bound

this question relates to the requirement for achieving CRLB. I know that for a random sample $Y_1, \ldots, Y_n$, an estimator $U$ of $g(\theta)$ is MVUE (i.e. it is unbiased and also ...
1
vote
1answer
21 views

Reading P value from ANOVA table generated by R [duplicate]

I generated an ANOVA table in R and every boxes are in number except the P value shows "3.387e-05". What does that really mean?
0
votes
1answer
22 views

Definition of true density

I am reading a paper and it talks about true densities, I mean they talk about obtaining densities from data and later compare them with the true density I want to know how can I obtain a true density ...
0
votes
0answers
16 views

Required sub-chapters or more materials needed to learn Statistical Inference other than my textbooks

My school is using new curriculum now and chapter "Statistical Inference" appears in my textbooks. Now I'm at second level of senior high school. I have two books, each of them has own sub-chapters ...
0
votes
1answer
45 views

Kruskal Wallis - Effect size

I analyse 4 algorithms and 3 sets of metrics for each algorithm in which I apply the non-parametric Kruskal-Wallis test for each metric to detect any differences in performance between these ...
1
vote
2answers
24 views

Testing $H_0 : \mu_x \neq \mu_y $, in a company that markets two brands of latex paint.

A company markets two brands of latex paint regular and a more expensive brand that claims to dry an hour faster. A consumer magazine decides to test this claim by painting ten panels with each ...
-1
votes
0answers
20 views

Write an expression for Pr[|X¯N | > t] in terms of µ, σ2 , and Φ(·), given random sample of observations? [on hold]

Suppose that X1, ..., XN is a random sample of N(µ, σ2) observations. Let Φ(·) denote the standard normal cdf. Let X¯N denote the sample mean. Write an expression for Pr[|X¯N | > t] in terms of µ, ...
-1
votes
0answers
26 views

Statistics Question [closed]

I got this problem on a recent homework assignment. I understood how to do parts a and c, but cannot do part b at all. Any help would be really appreciated here.
1
vote
1answer
22 views

Subpopulations of an island (Bayes theorem?)

Help appreciated here. An island with 2 regions, I and II, has 4 types of individuals: AX, AY, BX and BY, for which we know their exact total nos. Here A-B-X-Y are simply traits, e.g., A=Male, ...
1
vote
1answer
15 views

Paired and unpaired data-Statistics/Hypothesis testing

I'm getting a bit confused about paired and unpaired data, for example in this question I don't understand how this data is paired. If it was the same steel pipes that were left uncoated first in ...
-2
votes
0answers
14 views

Statistical question [closed]

prepare a two way analysis of variance table and carry out the test for the significance of difference in the mean sales due to i) 3 different salesmen ii) 4 different georaphical regions, where ...
0
votes
0answers
19 views

how to find $X^2_{0.95,14}$, $P(X^2_{9} \geq y) = 0.99$ in a TI-84 calculator?

Can someone please show the steps in how to find $X^2_{0.95,14}$ in a TI-84 calculator? My professor does not want us to use a statistics table, but to know how to use the calculator in quizzes and ...
0
votes
0answers
9 views

Hypothesis Question

Consider the following hypothesis: $H_{0}:\mu\leq3000$ vs $H_{a}:\mu>3000$ A sample size $n$ must be decided so the risk of a type 1 error is at most 1%, and also so that if the value of ...
0
votes
1answer
43 views

What's in a name? (Sum of Squares)

I have always believed that in order to fully understand and appreciate the mathematical subtleties and ideas behind a certain concept is to understand the name given to it. For now, can someone ...
0
votes
2answers
117 views

Baysien Inference and error probablility

Let $\Theta$ be a Bernoulli random variable that indicates which one of two hypotheses is true, and let $P(\Theta=1)=p$. Under the hypothesis $\Theta=0$, the random variable $X$ is uniformly ...
0
votes
0answers
26 views

Interpreting what this means in a paper - significantly different at the .05 level?

I am having a hard time interpreting what something means in a paper I'm trying to get through. If you care, this is the paper: Gender Differences in the Effect of Education on the Slope of ...
1
vote
1answer
34 views

Bias of $\sigma^2$ estimator

I need to find the bias of $\frac{\sum(x_{i}-\bar{x})^2}{n+1}$ for $\sigma^2$. To do so, one must take its expectation but add and minus $\mu$ from the summation part so we can bring $\sigma^2$ into ...
0
votes
0answers
72 views

Analytical Statistics Word Problem [closed]

I got parts a and b on this recent class assignment, but c onwards are a real challenge for me. Any kind of help would be greatly appreciated. Im totally stuck as to how to approach the rest of this ...
2
votes
0answers
42 views

t-distribution and Degrees of freedom

Why t- distribution have n-1 degrees of freedom? I know that it is used when population variance is not known but what determines n-1
1
vote
0answers
17 views

How can we have $T_n \xrightarrow{\mathbb P_\vartheta} \vartheta$ if $T_n$ are defined on different spaces?

Here is how I understand the standard parametric model in statistical inference: We have a r.v. $X:\Omega \to \Psi$ which has some known to us distribution yet the exact parameter is unknown to us. ...
3
votes
1answer
38 views

When does the variance of a consistent estimator go to zero?

I came across the following statement (marked as true) in multiple-choice section of an old exam: The variance of a consistent estimator goes to zero with the growing sample size. As far as I ...
0
votes
0answers
13 views

Big O p Question about Eigenvalue of Random Matrix

Suppose $S_1, S_2, \dots$ are a sequence of random symmetric matrices in $\mathbb{R}^{d\times d}$. Suppose we know that $|\lambda_\max(S_n)| = O_p(b_n)$ and also that $|\lambda_\min(S_n)| = O_p(b_n)$ ...
0
votes
1answer
19 views

How can he assume SD of population equals to SD of sample means?

I'm referring to this KhanAcademy video: https://youtu.be/bekNKJoxYbQ?t=445. My question: How can he approximate the SD of the population to be equal to SD of the sample means? Isn't that SD of the ...
-2
votes
0answers
42 views

Find the maximun likelihood estimation [closed]

Let $X_,\ldots , X_n$ be iid normal random variables with distribution: $$P(X=m) = \frac{a^m}{(1+a)^{m+1}},\quad m=0,1,2,\ldots$$ Where $a$ is the unknown parameter. How should I find the maximum ...
3
votes
0answers
33 views

showing that $E[(\hat\theta -\theta)^2] \lt Var(\bar X)=\dfrac{1}{n}$. [closed]

Suppose $X_1, X_2, \dots, X_n$ are i.i.d $N(\theta, 1),\theta_0 \lt\theta$ , Find the MLE of $\theta$ and show that it is better than the sample mean $\bar X$ in the sense of having smaller mean ...
1
vote
0answers
21 views

Conditional Probability/Expectation in the EM algorithm

I'm doing a study in which I measure data under a random censoring process. The observed data which may be interpreted as the lifetime of a subject, is denoted by $t$, with the censoring variable $c$ ...
0
votes
0answers
14 views

calculating the risk function $max(\bar{X},2)$ under Squared error loss function

suppose $X_1,X_2,\ldots,X_n$ be a random sample of $N(\theta,1), \theta>2$. how can I calculate the risk function $max(\bar{X},2)$ under Squared error loss function
0
votes
2answers
26 views

distribution of the indicator function of poisson

Let $X_1,\dots,X_n$ be independent random variables with poisson distribution Given indicator function $$ U_i=\left\{ \begin{aligned} 1 && X_1 \ = 0\\ 0 && X_1 >0 \end{aligned} ...
0
votes
0answers
13 views

Some true/false statements about MLE and UMVUE for a normal distribution

Let $X_1,X_2,...,X_n$ (assume $n\geq 2$) be a random sample from an $N(\mu,\sigma^2)$ population where $-\infty<\mu <\infty$ and $\sigma^2>0$ are unknown. Which of the following statements ...
0
votes
1answer
14 views

To find the distribution of the random variable based on uniform distribution

Let $X_1,X_2,...,X_n$ be iid $U(-5,5)$ random variables. Then the distribution of the random variable $Y=-2\sum\limits_{i=1}^{10}\log(|X_i|/5)$ is (A) $\chi_{10}^2$ (B) $10\chi_{2}^2$ (C) ...
0
votes
1answer
29 views

Calculating 95% confidence interval for mean for a normal population

Consider a normal population with unknown $\mu$ and variance $\sigma^2=9$. To test $H_0:\mu=0$ against $H_1:\mu\neq 0$, a random sample of size 100 is taken. Based on this sample, the test of the form ...
0
votes
0answers
18 views

estimation of the parameters of generative process modelling second-price-auction

The generative process: There are 2 entities (A,B) entity A - is the exchange performing second-price-auction entity B - is somebody who is trying to understand the distribution-of-the-value people ...
2
votes
1answer
20 views

To calculate variance, given conditional distribution

Let Y be an exponential random variable with mean $\frac{1}{\theta}$, where $\theta>0$. The conditional distribution of X given Y has Poisson distribution with mean Y. Then, the variance of X is ...
1
vote
1answer
35 views

UMVUE for pdf $f_{\theta}(x) = \theta e^{-\theta x}, x>0$

Let $X_1,\ldots,X_n$ be a random sample from a pdf $f_{\theta}(x) = \begin{cases} \theta e^{-\theta x}, & x>0 \\ 0, & \text{otherwise} \end{cases}$, where $\theta>0$ is an unknown ...
1
vote
0answers
16 views

Fisher Expected Information for a Gaussian Process model

Suppose I have a two dimensional Gaussian process model (GP), defined by a squared exponential correlation function s.t: $$R(x_{i},x_{j}) = \exp\left(-\frac{|x_{i} - x_{j}|^2}{2}\right).$$ I am ...
0
votes
0answers
4 views

Most Powerful Test and Rejection Region of Gamma Distribution [migrated]

Let $X_1,...,X_n$ be a random sample from a Gamma $(\alpha,\beta)$ population, where $\beta>0$ is a known constant. The rejection region of the most powerful test for $H_0:\alpha=1$ against ...
2
votes
1answer
16 views

Calculating power of a Hypothesis Testing Problem based on Uniform distribution

Consider the problem of testing $H_0:a=0$ against $H_1:a=1/2$ based on a single observation X from U(a,a+1). The power of the test "Reject $H_0$ if $X>2/3$" is (A)1/6 (B)5/6 (C)1/3 (D)2/3 ...
0
votes
0answers
8 views

Standard Error in Sampling Distribution

I want to understand that why while calculating probability on a sample data we consider standard error not the standard deviation of the sample. I know that standard error is the variance of sample ...
0
votes
0answers
33 views

two-parameter exponential distribution

Now, I have some problems about the distribution of random variable. In my work, let $X_{i}$ for i= 1 to n be iid random variable from two-parameter exponential distribution. We known the Mgf of X is ...
1
vote
1answer
33 views

What does “except null set” mean?

I am watching a video on sufficient statistics here. In the video, the sufficient statistics is defined as follows. I am puzzled by the part in the red box. I know it is describing some trivial ...
2
votes
2answers
36 views

Confidence Intervals that Contain the Mean: Designing an Activity

This past Wednesday, I had my stat class do the following exercise: Roll a fair 6 sided dice 25 times. Take the sample mean of the face value. Using the standard deviation of the uniform ...
0
votes
1answer
21 views

A question in the proof of Rao-Blackwell theorem

This could be a naive question but I am just puzzled. I am learning the following proof of Rao-Blackwell theorem but get puzzled by the equation in the red box. Why the two expectations can be reduced ...