A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.

learn more… | top users | synonyms (1)

0
votes
1answer
38 views

Sum of iid random variables

Let $X_1, X_2,...,X_n$ be iid random variables. Let $Z_1, Z_2, Z_3$ be defined as $X_1, X_1+X_2, X_1+X_2+X_3$ respectively. Are $Z_1, Z_2$ and $Z_3$ also iid's? The question is based on renewal ...
1
vote
0answers
36 views

How to compute the probability of $P(a|b,e)$ given $P(a|b), P(a|e)$ and $A$ independent of $B$?

The following is given: $$ \begin{align} P(b) &= P(e) = 0.1\\ P(a|e) &= 0.2\\ P(a|b) &= 0.95\\ P(a|\neg b, \neg e) &= 0\\ B &{\perp\!\!\!\perp} E \end{align} $$ Is there any way ...
4
votes
1answer
51 views

centering two variables X and Z makes cov (X,XZ) = 0

I've read that centering two normal (or symmetrical) variables $X$ and $Z$ affects correlation of centered $X$ with interaction term $X\cdot Z$ in such way, that this correlation $cor(X-EX, X\cdot Z)$ ...
0
votes
0answers
7 views

To sketch a “typical” plot of a specific time series model

Let X have a distribution with mean $\mu$ and variance $\sigma^2$, and let $Y_t = X$ for all t. Sketch a “typical” time plot of $Y_t$. My thoughts: This process $Y_t$ is stationary with mean $\mu$, ...
0
votes
1answer
29 views

How to solve this Expectation of log of random variable

This may seem a trivial Question but I am confused and never come across this kind of expression where I need to simplify for a function of a random variable $R$. I have an expression $E\bigg ...
0
votes
0answers
10 views

Hidden Markov Model vs Markov Transition Model vs State-Space Model…?

For my master's thesis, I am working on developing a statistical model for the transitions between different states, defined by serological status. For now, I won't give too many details into this ...
14
votes
2answers
921 views

Why are “time series” called such?

Why are “time series” called such? Series means sum of a sequence. Why is it time Series, not time sequence? Is time the independent variable?
1
vote
1answer
64 views

Question on a probability question

I have this question for a test: A judge is 35% sure that Tim commited burglary. The witness would lie at a probability of 0.25 if Tim is guilty but would tell the truth if Tim is innocent What ...
2
votes
0answers
86 views

Unsure in taking the derivative in order to derive the MLE : Is the estimator right?

The probability that there are $k$ observations within distance $t$ of $x$ can be written as : $$\mathbb{P}[N(t,k) = k] ={n-1\choose k}[f(x)V_t]^k[1-f(x)V]^{n-k-1}$$ The pdf of the distance from $x$ ...
3
votes
1answer
49 views

Testing correlation and the t-statistic used in Simple Linear Regression

Given $H_0$ : $\rho=0$ and $H_A$ : $\rho\neq0$, we use the test statistic $t_{n-2}$ , which is $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$. I have to show that $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ equals ...
5
votes
2answers
78 views

Standard error of regression coefficient without raw data

After searching here: Perform simple regression without raw data I am still curious about this. Is it possible to derive the standard error of a regression coefficient from summary data alone? ...
0
votes
1answer
25 views

Is Randomized Complete Block Design a two-way anova?

Isn't Randomized Complete Block Design a two-way anova ? Can it be one-way ? As far i understand, since there is treatment effect and also block effect in RCBD, it is two-way anova. But can it be ...
1
vote
1answer
49 views

Algebraic manipulation of $Var(Y|X)=E[(Y-E(Y|X))^2|X]$

Q: Show that $Var(Y|X)=E[(Y-E(Y|X))^2|X]$ is equal to $Var(Y|X)=E[Y^2|X]-(E[Y|X)]^2$. Answer: I know I have to use the law of iterated expectation to get to the second statement but I am having ...
2
votes
2answers
74 views

Bayesian Linear Regression

I have the following question concerning Bayesian linear regression on my machine learning assignment: Consider $f = w^Tx$, where $p(w) ∼ N(w | 0, Σ)$. Show that $p(f | x)$ is Gaussian. I ...
1
vote
1answer
21 views

Randomized Block ANOVA Model: Intermediate Steps

While reading through my lecture notes, I came across a randomized block ANOVA model and some assumptions. How did the authors get to these assumptions (Expectation and Variance) from the given model? ...
2
votes
1answer
57 views

Bayesian linear regression question

I am doing a problem on Bayesian regression but I'm having a lot of trouble with it. Here is the question: Consider $f=w^Tx$, $p(w)\sim N(w|0,\Sigma)$. Show that $p(f|x)$ is Gaussian. Find the mean ...
1
vote
0answers
28 views

A math proof within a question about homogeneous Poisson process

We know that a homogeneous Poisson process is a process with a constant intensity $\lambda$. That is, for any time interval $[t, t+\Delta t]$, $P\left \{ k \;\text{events in}\; [t, t+\Delta t] \right ...
3
votes
0answers
47 views
+50

Unable to understand the paper in computing Fisher Information and the CRLB

I am unable to follow the steps needed to derive the Fisher Information matrix and the CRLB of an autoregressive model from the observations $x$. The AR process is excited by non-Gaussain sequence, ...
1
vote
0answers
22 views

Proof about an Inhomogeneous Poisson Process

We know that an inhomogeneous Poisson process is a process with a rate function $\lambda(t)$. That is, for any time interval $[t, t+\Delta t]$, $P\left \{ k \;\text{events in}\; [t, t+\Delta t] \right ...
3
votes
1answer
68 views

Show that the sample covariance converges in probability to the $Cov(X,Y)$

Suppose we are given $[(Y_i,X_i)]^{n}_{i=1}$ which is a random sample from the joint distribution of $(Y,X). Show that the sample covariance converges in probability to the $Cov(X,Y)$ My thought ...
0
votes
0answers
4 views

How was the explicit closed form for this implicit function derived? [migrated]

The problem comes from reading this [0] paper but I think I can express it in a self contained question. Consider the implicit function $H(z)$ defined by the relation: ...
4
votes
2answers
60 views

If $E[Y|X]=a$ for some constant $a\neq 0$, then does $cov(X,Y)=0$?

I'm currently working on the following problem: Q: If $E[Y|X]=a$ for some constant $a\neq 0$, then does $cov(X,Y)=0$? Now I am quite lost as to how to do this problem as the question does not ...
0
votes
0answers
24 views

Probability distrubution of 3 products

A lightbulb factory produces bulbs in 3 qualities. 50% of production is Low quality, 30% average quality, 20% good quality. A randomly selected lot of 4 bulbs gets tested. Low quality lights have a ...
8
votes
5answers
350 views

Intuitive explanation of convergence in distribution and convergence in probability

I am quite unsure of the intuitive difference between a random variable converging in probability versus a random variable converging in distribution. I've read numerous definitions and mathematical ...
0
votes
0answers
20 views

Level of measurement [closed]

You are working with older adults in a geriatric care unit. Your nurse manager asks you to measure the intake of desserts in the dining hall. You report that 3 adults consumed 0 desserts, 27 adults ...
1
vote
0answers
22 views

why is the incomplete log-likelihood difficult to optimize

I am trying to teach myself the expectation-maximization algorithm and the texts say the EM is particularly useful when the incomplete log-likelihood i.e. $P(X|\theta)$ where $\theta$ are the ...
3
votes
0answers
38 views

Finding a test statistic when you don't know the distribution?

I am working on this problem from my class and it has stumped me for a while now. I will show a picture of the problem and then my work/thoughts: Now we are not given the individual distribution of ...
0
votes
2answers
34 views

Why is this test statistic standard normal? Simple question

My textbook just says that the following test statistic is normal without actually going through the derivation. Here is the problem: Suppose that $X_1...X_n$ are iid RV with each being ...
3
votes
1answer
23 views

Distribution of test statistic under null and alternative

I am currently reading my econometrics notes and there is an example that has really stumped me. The example has an answer with it but I do not understand a few things: Now what I do not understand ...
1
vote
1answer
46 views

How to compute the sum of a mixture distribution with another distribution?

I need to find the pdf of x, $f_x(x)$ which is the sum of two random variables $u$ and $w$ and they are independent. I have found the pdf but I am unsure if it is correct or not, the expression is ...
1
vote
1answer
29 views

Comparison of two means within the same group

I created a pretest before my main study. The goal of the pretest is to find two brands that are equal in terms of liking and familiarity. I computed the variables in SPSS and I was wondering if I ...
0
votes
0answers
35 views

Compare more than two means

New in statistics and I need your help regarding an easy question I think. I'm running out of time for my assignment so I kindly ask you to help me if possible. I'm running a pretest and the main ...
5
votes
2answers
70 views

What's the model representation for the first difference of a local level model?

This is my first exercise for space state models and I've a few questions I'd need to resolve before I actually start doing the exercise. Unfortunately, I'm self teaching (I have no professor to ask) ...
0
votes
0answers
16 views

Finding a consistent estimator mathematically

This is my first post on this website so hopefully everything will go smoothly. Let me first ask the question, then go over my problem. Q: Suppose that we are given $({X_{1i},X_{2i}})$ which is a ...
1
vote
1answer
22 views

Find the sampling distribution of the MLE of the uniform distribution [duplicate]

The MLE is $ \theta = max [x1,...,xn] $ And $ P(max [Xi] < t) = P(Xi < t)^n = P(t/\theta) $ But the question asks me to show that $ P(max[Xi]< t) = (min[\theta, t]/ \theta)^n * I[t>0] $ ...
-1
votes
1answer
24 views

Estimator $\gamma = \sum a_i\times x_i$ , where $X_i \sim \exp(t_i \theta )$ Show $\gamma$ is unbiased if $\sum a_i/t_i = 1$

I'm getting really confused with the estimators in this question! $X_i \sim \exp(t_i \theta x)$ where $t_i$ are positive constants. The MLE for $\theta = \frac n{\sum t_i x_i}$ And $\phi = ...
1
vote
1answer
37 views

Density Function Estimation

Given a sample of $n$ observations, which are assumed to be $i.i.d.$ and generated from a continuous probability law. Consider the question of estimating the density function $f(x)$. There are two ...
3
votes
1answer
90 views

Show that $\min(U,1-U)$ and that $\max(U,1-U)$ are uniform

Let $U$ be uniform on $(0,\ 1)$. Show that $\min(U,\ 1-U)$ is uniform on $(0,\ 1/2)$ and that $\max(U,\ 1-U)$ is uniform on $(1/2,\ 1)$. I'm not sure how to approach... the only hint i have is that a ...
2
votes
2answers
328 views

Metropolis-Hastings Algorithm within Gibbs Sampling

I have this $f$ function below. $$ f(x_1,x_2)\propto \left(\dfrac{x_1}{x_2}\right)\left(\dfrac{\alpha}{x_2}\right)^{x_1-1}exp\left\{-\left(\dfrac{\alpha}{x_2}\right)^{x_1} \right\}I_{R^+}(x) $$ where ...
2
votes
0answers
29 views

parameter and prediction confidence intervals

We have a correctly specified linear model $z = x\beta + \varepsilon$ with 100 independent observations. Given: $y = e^z$, $\sigma^2 = 4$ (assumed to be known), sample means $\bar{x} = -3$ and ...
5
votes
3answers
87 views

Computing the Variance of an MLE

Suppose we have i.i.d. $n$ observations $(X_1,X_2,...X_n)$ from a population with density $$f_\theta(x)=\begin{cases}\theta x^{\theta-1}&\text{ if }0\leq x\leq ...
0
votes
0answers
31 views

Do two samples represent two different populations?

Which statistical method could be used to determine whether two samples represent two different populations?
0
votes
0answers
18 views

Compare two independent samples with one variable

It is assumed that in computer programming courses, students programming in pairs will have better grades than students programming alone (solo-programming). After collecting data about the grades of ...
-1
votes
1answer
30 views

Which K-mean algorithm I have to use for this problem?

Perform a k-means Clustering (non-iterative algorithm) using k=2 randomly initialised centroids (cluster prototypes), and the Euclidean distance. At the moment I manage to understand you can use ...
0
votes
0answers
18 views

applying statistics in “filling in” a data set?

Let me first say that my professional role is that of a mid level OLAP/OLTP developer (lesser experence with OLTP). Ive only had business statistics in school many years ago and I am currently taking ...
0
votes
1answer
50 views

Compare two groups

In an experiment, 20 project experts (10 from technical roles and 10 from non-technical roles) were instructed to estimate the effort required to complete a web development project.They could use ...
0
votes
3answers
85 views

Programming Language to Use (Statistics Beginner Warning) [closed]

The options I've seen and am looking at as possible in some combination here: R Java Python Matlab Visual Basic + Excel VBA SAS C/C++ C# What I have experience in: Java JavaScript HTML/CSS (Also ...
4
votes
3answers
89 views

Violation of Gauss-Markov assumptions

Which of the Gauss-Markov assumptions is violated in this picture? If all other Gauss-Markov assumptions are satisfied, is the OLS estimator for $\beta_1$ unbiased and consistent? Why? In the ...
3
votes
2answers
60 views

Possibility of solution in overdetermined system of moment conditions

Hayashi, in page 207-208 of his book Econometrics, ex.3 (see hint), discusses the possibility that when referring to the moment conditions that will determine the estimator formula, having an ...
2
votes
0answers
11 views

Half-Normal Plot of Coefficients from Binary Factorial Experiments

After I wrote this all up I debated whether or not I should post it because I think I know the answer to this question (after looking at the two models I'd end up with), but since I don't really know ...