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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Calculate the auto correlations and mean of the following time series [on hold]

$$Y)t=0.7+0.4Y_t−1+0.12Y_t-2+Z_t$$ calculate $E(Y_t)$ Also calculate the auto correlations $p_1-p_4$.
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6 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 ...
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22 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 & ...
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13 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 $\lambda = 2$ ? ...
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2answers
32 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 ...
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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 ...
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1answer
16 views

Statistical Intervals - Confidence Intervals Homework Help

The following is a homework problem from my textbook, I am totally confused on how to solve this problem. Please help!!!!! Let $X_1, X_2, ………, X_n$ be a random sample from a continuous probability ...
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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 ...
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17 views

Calculating expectation using Gamma and Exp R.V.'s

I'm working on a homework problem from Hogg (7.3.4) and am a bit stuck. I need to calculate the following expectation: $$ E(Y) = \int^{\infty}_0 \frac{2}{\theta}y ...
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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 ...
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15 views

Monte carlo formula to compute the approximation of variance of MLE

In the book of "Monte Carlo Statistical Methods", the book gives an approximation formula for the variance of MLE, Later on, the book mentions that this approximation formula can be written as ...
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2answers
21 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 ...
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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 ...
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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 ...
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1answer
24 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 ...
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1answer
21 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 ...
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1answer
25 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 ...
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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: ...
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17 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: ...
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1answer
10 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: ...
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2answers
30 views

How to tell if two samples come from the same probability distribution?

I have two distributions (generated from binned data) and wish to answer the question: Do they come from the same underlying distribution? I don't have the form of the underlying distribution. Edit: ...
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1answer
26 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 ...
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1answer
24 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 ...
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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.
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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 ...
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1answer
37 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 ...
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1answer
23 views

MLE Proof - Hogg Theorem 6.1.1

The theorem is that under certain assumptions (regularity conditions): $$ \lim_{n\to \infty} P_{\theta_0} [L(\theta _0, X) > L(\theta, X)]=1, \,\,\forall \theta \neq\theta _0$$ What I'm having ...
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23 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 ...
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11 views

How do I remove emotional bias in rating survey questions? [migrated]

I want to do a survey about the quality of a slot game. At the end of a game session (when player cashes out), there will be a question on screen: "Please rate the game on a scale of 1 to 5" Player ...
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1answer
14 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.
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7 views

Function of a complete statistic is complete

Quick question: If a have a statistic $T$ complete, is $a^T$ complete ($a$ constant)? In general, if a statistic is complete, then is every one-to-one function of it complete? Thanks.
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1answer
21 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 ...
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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 ...
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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, $X$ ...
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12 views

Calculate probability of total population from sample

I have a population of infinity size. Each Unit is Boolean(True/False). I take a random sample of size N of which M elements are True(and N-M are False). I'd like to know what the probability is that ...
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1answer
30 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 ...
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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 $\theta$?
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1answer
79 views

statistics inequality

Let $\theta$ be a discrete pararmeter and $\gamma_{n}$ be an estimator. Prove that for any $c>0$ we have that $$\text{E}[(\gamma_n-\theta)^2] \ge\Pr[|\gamma_n-\theta|>c]\cdot c^2$$
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1answer
11 views

Comparision between two random samples

I have the following simple random samples which denote the scores obtained by some students over $10$: Random sample A: 3.5 4.5 4.813 5.065 5.252 5.438 5.547 5.586 5.937 6.025 6.025 6.345 6.375 ...
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1answer
39 views

Expectation of the MLE $e^{-\frac{1}{\overline{X}}}$

I am having a bit of a problem with examining the properties of a maximum likelihood estimator. I feel like I am missing something simple, but I have been unable to find someone doing an example quite ...
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5 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 ...
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16 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 ...
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15 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 ...
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1answer
30 views

Regarding jointly multivariate normal X1,X2…X5

So I have a question from statistical inference that I need some help with: $X_1,X_2,...,X_5$ are jointly multivariate normal with means = $\mu_i$, variances = $\sigma^2_i$, correlation = $\rho$ ...
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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 ...
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62 views

Determining constant in a CDF

I have a question that I literally have no idea how to begin, I was hoping someone could help me: It says $X_1,X_2,\ldots,X_n$ is a sample from a distribution It says that the Cumulative ...
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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 ...
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2answers
52 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: ...
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68 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 ...
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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 ...