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0
votes
1answer
12 views

Wilcoxon Rank Test or T-Test? [duplicate]

What data analysis is better? or fit for my data? I've used Likert scale for my questionnaire (1-5) and I have 387 respondents. Wilcoxon Rank Test or T-Test?
1
vote
1answer
14 views

How to write an AR(2) stationary process in the Wold representation

I managed to write an AR(1) process in the Wold representation with help from the geometric series. I am having trouble with a stationary AR(2). How could I do?
0
votes
0answers
17 views

Find variable k when given 2 marginal distributions

Given $f_x(x) = \frac{k}{1+4x}, -\infty<x<\infty$ and $f_y(y) = \frac{k}{1+4y} , -\infty<y<\infty$, find $k$. $x,y$ are independent random variables. What I've tried: Since the variables ...
0
votes
0answers
27 views

Why are Coefficient of each other principal component cannot be all of the same sign?

For the covariance matrix $\Sigma \in \mathcal{M}_{p,p}$, a positive-definitie (non-singular) matrix with its elements $\sigma_{ij} >0$ for all $i,j = 1,2,...,p$. How do I prove that the ...
5
votes
0answers
30 views

Is the negative binomial not expressible as in the exponential family if there are 2 unknowns?

I had a homework assignment to express the negative binomial distribution as an exponential family of distributions given that the dispersion parameter was a known constant. This was fairly easy, but ...
0
votes
1answer
42 views

Help for Binomial Distribution question

I am having issues with understanding a question on an assignment: A test for the presence of a certain disease has probability 0.05 of giving a false-positive reading and probability 0.04 of ...
0
votes
0answers
21 views

Markov Chain Absorbing States Query

If given the Markov Chain with state space ${0,1,2,3,4,5,6}$ and transition probabilities $p(0,0) = 0.75$, $p(0,1) = 0.25$, $p(1,0) = 0.5$, $p(1,1) = 0.25$, $p(1,2) = 0.25$, $p(6,0) = 0.25$, ...
0
votes
1answer
12 views

Ensemble in stochastic process

I am learning a time series and forecasting course.In the book "The Analysis of Time Series by Chris Chatfield" it says that We only have single outcome of the process and a single observation on ...
0
votes
0answers
25 views

Is it always true that $E[E[X|Y]^2] = E[X|Y]^2$? [duplicate]

X and Y are random variables. So $E[X|Y]$ is conditioned on a random variable. Do we always have: $$E[E[X|Y]^2] = E[X|Y]^2.$$ I have the doubt because I know that $E[X|Y]$ is a random variable ...
1
vote
0answers
48 views

On $E[E[Y|X]|X]= E[Y|X]$

I am trying to simplify $E[YE[Y|X]|X]$ can I use this property: $$E[E[Y|X]|X]= E[Y|X]$$ If yes I have never seen a Proof of this property (that seems very reasonable), could I have a reference? If ...
1
vote
0answers
28 views

on the minimization of: $E[((Y-f(X))^2|X]$ [duplicate]

I am having troubles solving this exercise: Deduce that the random variable $f(X)$ that minimizes $E[((Y-f(X))^2|X]$ is $$f(X)= E[X|Y]. $$ I proceeded in this way: $$E[(Y-f(X) + E[Y|X] - ...
0
votes
0answers
34 views

Standard error of slope estimator

Can someone please help explain this. I know the answer is a). Or provide a link with more information. The slope estimator, β1, has a smaller standard error, other things equal, if a) there is ...
0
votes
1answer
122 views

Probability Homework Question

A researcher is conducting a survey of county residents in a Midwestern state. Foolishly, she uses lists of registered voters as a sampling frame and randomly draws phone numbers and addresses from ...
0
votes
0answers
29 views

Help in calculating OLS estimators under certain constraints/modifications

I am new to these forums and to econometrics as a whole. I was hoping someone would be able to give me a nudge in the right direction with this problem. I've done extensive research both online and in ...
0
votes
0answers
12 views

how to offer recommendation? comparison of satisfaction between two groups?

My research is "level of satisfaction in relation to customer service: comparative study between 2 fast foods my questionnaire consists of 19 questions. I'm using SERVERF, the 5 dimensions. 8 ...
0
votes
1answer
349 views

Posterior Probability Question

a) Your initial belief is that a defendant in a court case is guilty with probability 0.5. A witness comes forward claiming he saw the defendant committed the crime. You know the witness is not ...
1
vote
2answers
74 views

data analysis, dissertation of thesis? help please?

I'm having a problem with my dissertation. My research is "level of satisfaction in relation to customer service: comparative study between 2 fast foods my questionnaire consists of 19 questions. ...
2
votes
4answers
70 views

Counterexample against binomial assumptions

The question is from a Master-level Probability Course. It is well known that the underlying assumption for the binomial distribution is that there are n independent Bernoulli trials. More ...
0
votes
1answer
36 views

Using R to calculate qt (t-dist) using qf(f dist) help?

I am having quite some trouble using R to calculate, say, qt(0.975,6) using qf instead of qt. I know the relationship between the t-distribution and the f-distribution which I understand as follows: ...
0
votes
0answers
9 views

How to prove this claim in real analysis [migrated]

E is a set of positive outer measure, how to prove that there must be a bounded subset of E that has positive measure?
0
votes
0answers
23 views

Expected value of a squared fraction of Y

I need to work out the following: $$ E[(\frac {Y(x+h)-Y(x)}h)^2] $$ I've already worked out the below and am supposed to use it to work out the above. $$E[(Y(x+h)-Y(x))^2]$$ I'm not able to find ...
1
vote
1answer
18 views

Is X a negative binomial? ( Tosses of dice)

Two dice are tossed independently until each pair has appeared at least once. Find the expected number of tosses needed and the standard deviation of this number of tosses. My attempt Let X be the ...
0
votes
1answer
31 views

Resources for when population data is available

There are hundreds if not thousands of textbooks that detail how to make population inferences from sample. However for almost all my applications at work I have the entire population of data for ...
2
votes
1answer
31 views

How to check my data set is following non-linear to linear regression?

I have two data sets with y and X1,X2,X3,....,X6 all Xi's are independent variables and y is dependent variable. Instructor said that one data set will follow linear regression and other will follow ...
4
votes
0answers
40 views

Question 10.9 from Bayesian Data Analysis, what does accuracy mean here?

I'm doing an independent study in Bayesian Statistics following some chapters from BDA3. When solving the first question from Ch 10 I got stuck. It says: [If] a scalar variable $\theta$ is ...
0
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0answers
26 views

demostrate Jensen's inequality (i think) [duplicate]

Please any help is very good. I was trying to start with the definition of expected value but I don't know how to finish.
2
votes
0answers
17 views

Error of bounded mean estimation with quantization

I have a distribution whose mean $\theta \in [0,1]$. Given $n$ observations, I compute the sample mean (say $\hat{\theta}$) and quantize it to accuracy $\frac{1}{n}$ (basically I can use only ...
2
votes
1answer
33 views

Sufficient and complete statistic

Let $ X_1, ... , X_n $ be i.i.d random variables with pdf given by $$f(x;\theta) = \exp(-(x-\theta))I_{(\theta, \infty)}(x)$$ It is asked to find a sufficient statistics for $ \theta $ and to verify ...
-1
votes
0answers
49 views

Calculate the mean and variance of two random variables from their density functions

How do you calculate the mean and variance of two random variables X~F(m = 3, n = 6) and Y~F(m = 8, n = 6) from their density functions using R?
2
votes
1answer
19 views

Conditional Binomial Question

Lost touch on some basics: $X \in Bin(n,p)$. Suppose that we know $P(X \ge l)$. Can we get a distribution for $P(X=x | X \ge l)$, $l \le n$? I would assume we use bayes rule and find $P(X=x, X \ge ...
3
votes
1answer
26 views

Question about definition of random sample

In my statistics class, we're just beginning to talk about (point) estimation. I have a small question that might actually be due more to notation/definition than anything very conceptual: Say you ...
0
votes
0answers
17 views

how one independent variable affects other variable in multiple regression

I have a two independent predictors in regression equation "X1" and "X2". X2 is categorical hence 1,0 is the allowed values. I have to find how X1 get affected based on value in X2 in following ...
0
votes
1answer
25 views

Probablity calculation for at-least clause case

I saw the question: What is the probability of 1 out of 5 randomly selected people agree with the statement that men having more right for job compare to women? ...
0
votes
1answer
28 views

Find MLE by combining two different experiments

I am trying to solve the following problem on an assignment. Anna has two dice. Die $F$ is fair: it rolls $1,2,3,4,5$ or $6$ with equal probability $\frac{1}{6}$. Die $D$ is dodgy: Anna suspects ...
4
votes
1answer
83 views

null hypothesis change

I've done loads of hypothesis tests for the mean (normal distribution) where the null hypothesis is of the form $H_{0}=a$. Now I've come across one where the hypotheses are like $H_{0}{\leq}a$ and ...
0
votes
1answer
54 views

Homework problem. What is the answer supposed to look like?

I am taking a statistics course this semester, and this is part of our first homework assignment, only I don't know what the answer is even supposed to look like. When the process is functioning ...
2
votes
1answer
56 views

Design of Experiments

Suppose a dermatologist wants to study the effectiveness of two different preparations of a skin lotion using two different forms of application, such as one versus two applications per day. She has ...
0
votes
0answers
30 views

How do the various distributions work into machine learning

I'm a student who recently started taking a machine learning course and I'm trying to understand how the various distributions fit into the whole thing. From the research I've been doing it seems the ...
2
votes
1answer
52 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
1
vote
0answers
16 views

Sample of one, extermination of fruit flies and daily life challenges

First of all, I'm very well aware that a sample of one is ridiculous in any normal scenario in the domain of statistics, and I know that any rationale from this would probably only have esoteric ...
1
vote
0answers
14 views

Fractional Factorial Design with Highest Resolution

In the book Design and Analysis of Experiments by Douglas C. Montgomery , it is written that We usually like to employ fractional designs that have the ...
2
votes
1answer
103 views

drawing balls from an urn

Suppose there are 7 golf balls in an urn and you draw balls in 3 stages without replacement. First you draw 2, then 3, and then the remaining 2. How many ways are there to do this? I believe the ...
3
votes
1answer
37 views

Covariance of $cov(5W_7+6W_9,W_7)$ where $W_t$ is a standard Brownian motion

I'm having trouble deducing the value for the problem in the title. Here is what I have done so far. (Given a standard Brownian motion (BM) $W_t, t\geq0 $ with $W_0 = 0$ and $\sigma^2=1$) The ...
3
votes
0answers
52 views

How to find an appropriate sample size given information about the CV?

You are planning to collect a (simple random) sample to estimate the mean of a non-negative random variable. It is known that the population coefficient of variation (CV) is 1.2. Use the central ...
2
votes
0answers
37 views

How to answer a clients question on “How accurate your logistic regression model is?”

There are various methods to test the model accuracy, but when it comes to clients you may face people who don't know AIC, ks-statistic, c statistic, confusion matrix, etc. So, how one should answer a ...
1
vote
4answers
1k views

How to add odds? (or how I got the wrong sandwich)

Jon and Frank ordered 2 footlong sandwiches, but instead got 4 6-inch sandwiches. Jon had ordered spicy italian, and Frank chicken teriyaki. The sandwiches aren't labeled and are wrap, so they can't ...
0
votes
0answers
12 views

Plotting of density estimates in matlab [migrated]

Given the biometric match scores, I am required to plot the graphs of estimated densities of matching genuine and impostor scores. Following are the graphs I got for genuine and impostor scores ...
0
votes
0answers
30 views

A non-negative definate matrix has a non-negative generalized inverse

I'm having trouble proving a N.N.D matrix has a N.N.D G-Inverse. So far I have: If we assume x = Az where x >= 0 and A is a nnd matrix. So if Y is a G-inverse than: x = Az = YAz = Yx >= 0 . Thus ...
1
vote
0answers
25 views

What method should I use to analyze data? [closed]

I failed to pass my regression analysis course as the lecturer didn't say what kind of analysis he wants on the data. The problem was: The index of biotic integrity (IBI) is a measure of the water ...
1
vote
1answer
40 views

Sum of Random Variables

As part of my statistical mechanics class, I'm trying to go through Kardar's statistical physics of particles and I'm having trouble with this one line: Consider the sum $X=\displaystyle ...