1
vote
3answers
36 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
0
votes
0answers
15 views

Proving a statistic is sufficient and NOT complete

Let X be a single observation from the distribution , $P(X=x)= \begin{cases} \theta, & \text{if $x$ =-1} \\ (1-\theta)^2\theta^x, & \text{if $x =0,1,2,3,...; 0<\theta<1$} \\ ...
0
votes
0answers
18 views

Sufficient statistic for normal distribution

Let X from a Normal distribution $(\theta,1)$. a) Find a sufficient statistic for $\theta$. b)Is $S_n^2$ sufficient for $\theta$ My answer for part a) The joint p.d.f= $1 \over (2\pi)^{n/2}$$e^{{-1 ...
0
votes
1answer
12 views

One and Two Tailed Independent T Test Questions

The city council for a small town has been receiving complaints from local law enforcement that citizens have been extremely uncooperative when pulled over for minor traffic violations. To remedy ...
1
vote
1answer
45 views

How to compute the unique MLE from an Exponential Family of Distributions?

Let $$ f(x;\theta)=\frac{1}{\pi} \frac{e^{\theta x}\cos(\theta \pi/2)}{\cosh(x)}, x\in{\mathbb{R}} $$ be a family of densities and which is clearly exponential family. Then what is the Maximum ...
0
votes
0answers
9 views

Conceptual doubt between observed values and samples

first of all, I know almost nothing about statistics (and I do no like it or I've never found a good reference). Apparently it is usual to write capital letters to denote random variables and small ...
0
votes
0answers
27 views

Which hypothesis test to use

Two identical machines are used to make a special coin. We want to know if they have the same variability. A random sample is taken from each machine : $$ \begin{matrix} MachineA & 135 & ...
0
votes
0answers
18 views

Poisson distribution confidence intervals and hypothesis

I think I have A and B correct but I have troubles with parts C and D. A) What is the p value if we suppose the following : finding golden apples in a tree follows a Poisson P(2) with $\lambda = 2$ ? ...
0
votes
2answers
36 views

probability question needs some help

suppose $X$ and $Y$ are independent and identically distributed random variables that are uniformly distributed on $[0,1]$ What is the PDF of $ W=Y-X $ i tried to draw a picture to illustrated it ...
2
votes
2answers
47 views

Does a proportion have to be a rational number?

Does a proportion have to be a rational number? For example, Assume we have a square with side $2$ units. We are throwing a circle of radius $1$ unit over the square. Let $X$ be the area of the ...
0
votes
1answer
19 views

What test could I use to test $\mu_1$ and $\mu_2$ instead of $\bar{x}$ and $\mu$?

A single sample $t$ test is only against a sample and a population correct? Can it test against a population and itself or two populations? ie $\mu_1$ vs. $\mu_2$....if not what tests would you use ...
1
vote
1answer
12 views

just a manipulation problem for statistics

I am a little bit confused when i was asked to Suppose $X_1, X_2,\ldots,X_n$ is a simple random sample from a continuous distribution with density function $f(x)$. Consider the new random variable ...
0
votes
2answers
24 views

Standard Deviation of Population from Sample.

I guess I am a little confused. I am doing t test statistics in my class. I think I know but I would love some insight. I am trying to get the estimated standard deviation for the population. These ...
0
votes
0answers
10 views

Is Expectation Propagation (EP) affected by the prior?

I understand EP by reading Minka's thesis: http://research.microsoft.com/en-us/um/people/minka/papers/ep/minka-ep-uai.pdf I'm trying to apply it to solve a Bayesian inference problem. However, I'm ...
0
votes
1answer
9 views

Hypothesis testing using chi-square distribbution

Four players meet weekly and play eight hands of cards. Over a year, one of the payers finds that he has won x of the eight hands with frequency fx given in the following table: x 0 1 2 3 4 5 6 7 8 ...
0
votes
1answer
25 views

Coefficient of variation - Help me decode this text

Doing some exercises I hit upon this wall of text: Coefficient of Variation should only be computed on ratio scales (i.e., data where there is a "true" zero, like temperatures in Kelvin, or ...
0
votes
1answer
23 views

Standard Deviation and Mean

take a look at this question: The sample from Population A has a mean of 35 and a standard deviation of 1. The sample from Population B has a mean of 45 and a standard deviation of 15. Which of ...
1
vote
1answer
27 views

Question on finding the Jacobian

I have a question which is as follows: The random variable U has the pdf $n \dfrac{u^{n-1}}{\theta^{n}}$ , $ 0 \le u \le \theta$ This is not independent of the parameter θ. Let Y=U/θ. Use the ...
0
votes
1answer
6 views

some knowledge about comare means of two group

I'm studying a bout statistic. I can compute very well. But i don't really know well. I want to know clearly about theory. And i have this problem: ...
0
votes
0answers
18 views

General procedure Vs pooled variance

When we compare means of two group. With independent sample, we have two method, but i don't know when use choose which one and when choose the other. Please help me classify them Two method are: ...
0
votes
1answer
13 views

How to choice between paired sample and Independent sample

I don't know how to decide to choose between pair and Independent to compare mean of two groups. Here is the excersise from a book: ...
-2
votes
1answer
27 views

Null Hypothesis and Confidence Intervals

I was told that If I reject the null hypothesis than my CI will not include the population mean. However the problem that I just did has a population mean of 2.72 and a lower CI of 2.5 and an upper CI ...
0
votes
1answer
31 views

Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.

CI(99) = xbar ± Zcv( σ / √ n -1 ) My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -. Here is the formula filled in (if it is the correct ...
0
votes
1answer
13 views

Why am I getting 84.25 instead of 97.68 for my Confidence Interval?

Why am I getting 84.25. I am doing 97.96*(6/sqrt[50-1]) = 97.96*(6/7) I am obviously not doing this correctly please help. It has been sometime since I have done any math.
0
votes
0answers
4 views

How to generate Effect Size (SMD with inverse variance) in cluster trial

I've been working on generating an Effect Size from a Cluster Randomized Controlled Trial. The ES that I have generated are different from those reported in the paper. Could someone help me find my ...
2
votes
1answer
38 views

Do I use the Standard Deviation of my sample or the population to find the standard error.

A professor is interested in determining if attending college influences the level at which an individual cooperates with the police. The professor is unsure if attending college will teach respect ...
0
votes
0answers
24 views

Nonrejection region- equivalently the area determined by confidence interval for $H_0: \hat \beta=\beta^*$

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 ...
0
votes
1answer
15 views

Find alpha when we know valuse of student distribution

Assume, we have $t_{1-\alpha/2,39} = 2.252401$. I don't know how can find $\alpha$. Please help me and how find it in R.
1
vote
1answer
28 views

What is the pivotal quantity

I had a question of two parts. I solved the first part but I am stuck on the second. Any hints or partial solutions would be greatly appreciated. a)$ X_1,....X_n$ are uniform iid on the interval ...
0
votes
1answer
28 views

some misunderstand about student distribution and R

I see on book : $t_{0.025,59}$ = 2.009 But when call qt in R. We have this result: qt(0.025,59) [1] -2.000995 I don't know why have different in here. As I think, $t_{0.025,59}$ must is ...
0
votes
0answers
13 views

Cross correlation computations

What are useful ways/formula for calculating sample cross correlations (i.e. correlation factors between individual components of two different random variables). Say I have two sample matrices, $X$ ...
0
votes
1answer
37 views

How do I find $\theta$ with bootstrap?

I have two vectors of known values $x$ and $y$. And the relationship between them is $y=\sin(\theta \cdot x)+\epsilon$, $\epsilon \sim N(0,1) $ . The question is how do I estimate $\theta$ with ...
0
votes
0answers
22 views

How to find MLE function?

I have two vectors of known values x and y. And the relationship between them is y=sin($\theta$$\cdot$x)+$\epsilon$, $\epsilon$~N(0,1) . The question is how i find the MLE function for $\theta$?
1
vote
1answer
84 views

statistics inequality

Let $\theta$ be a discrete pararmeter and $\gamma_{n}$ be an estimator. Prove that for any $c>0$ we have that $$\text{E}[(\gamma_n-\theta)^2] \ge\Pr[|\gamma_n-\theta|>c]\cdot c^2$$
0
votes
0answers
7 views

Stationary point of Unnormalized and Normalized KL-divergence minimization

I have encountered a problem, basically related to the http://arxiv.org/abs/1206.6679 . If I want to minimize the normalized KL-divergence KL(Q||P) with Q a multivariate Gaussian distribution. but in ...
2
votes
0answers
19 views

The distribution of the ith order statistic for discrete random variables

Assume $(X_i)_{i=1,...,n}$ are a sequence of real iid random variables with continuous density $p_x$. We know that $$Y:=\sum_{i=1}^n 1\{X_i\leq u\}\sim Bin(n,F_x(u)),$$ since $1\{X_i\leq u\}\sim ...
0
votes
0answers
16 views

Jeffery's prior - help

I'm studying Bayesian inference and looking at prior choices. Currently I have looked at Laplace's uniform prior choice and now I am trying to understand Jeffrey's prior. I am having trouble ...
0
votes
0answers
22 views

Multivariate Normal Variables

Sorry if this is a bit hard to read. Not entirely sure how to use the MathJax formatting on the site... The random variables $X_1, X_2, X_3, X_4$ and $X_5$ are jointly multivariate normal. Their ...
0
votes
1answer
40 views

Gaussian Approximation of an intractable distribution

I am currently encountering this problem: I have an intractable distribution and I want to minimize the KL divergence of this distribution and a multivariate gaussian distribution. So we just need ...
0
votes
2answers
55 views

Curve Fitting a Cyclical Pattern of Data

I'm analyzing phonological characteristics of the 22 letters used in the Hebrew alphabet, and assigned each letter an enumeration to see if they are organized based on place of articulation: ...
0
votes
2answers
69 views

What is this distribution???

Let $X_1, X_2, \ldots, X_n$ be a random sample from a population with $E(X_i) = \mu$ for all $i \in \{1,\ldots, n \}$. Define $ Y_i = \begin{cases} 1 & \mbox{ if } X_i < \mu \\ 0 ...
0
votes
1answer
13 views

Difference of parameters and arguments when dealing with statistics functions?

In 'classic' math when you have a function like $\sin (\theta)$ or $\cos (\pi)$ is pretty straight forward that both should have an argument and it's very simple to see that in this specific case the ...
3
votes
2answers
57 views

Distribution of the Objective Value and the Variables in an Optimization Program

For random variables $X$ and $Y$, where $X\sim f(X;\theta)$ ($X$ is drawn from some distribution with pdf $f$ which is parametrized by $\theta$ ), $Y=g(X)$; we know that we can find the pdf of $Y$ if ...
0
votes
2answers
46 views

Likelihood Function for the Uniform Density $(\theta, \theta+1)$

Let the random variable X have a uniform density given by $f(x;\theta)$~$R(\theta,\theta+1)$ What is the maximum likelihood function according to the samples $X_1,\ldots,X_n$? The question is much ...
1
vote
1answer
36 views

asymptotic normality and central limit theorem

Here's the question Can somebody explain the difference between asymptotic normality and central limit theorem? They seem very similar to me.
1
vote
1answer
34 views

log-likelihood ratio test question

Just a quick question When performing a log-likelihood ratio test, do I take log to both of the likelihood first or find the ratio first and take the log?
0
votes
0answers
18 views

Point estimation for two different group

Let θ be the difference in the mean precipitation from the two groups. Estimate θ. Estimate the standard error of the estimate and produce a 95 percent confidence interval. About mean, I use ...
2
votes
0answers
25 views

Normalizing multiple different features from unknown distributions

I'm doing some "exploratory" data analysis over a large set of classes/proteins, with a few hundred different features (I.E. Continuous variables) extracted from the data. The features are calculated ...
0
votes
1answer
40 views

Fitting a function with relative uncertainties

I want to find the parameters of a function that better fit some measurements. Usually, I use least squares. With it I am assuming that the best function is the most likely one and that the residuals ...
4
votes
1answer
47 views

Philosophy of Statistics (Likelihood Function)

Last week during statistics class, my professor asked us a few basic questions about statistics. We could answer most of them except these three questions that we could not provide him good answers. ...