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Questions tagged [self-study]

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

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21 views

Help me solve a homework problem (I have followed guidelines and included my steps) [duplicate]

Can someone help me with part B of this question please? I am completely stuck and do not know how to proceed. Hints rather than answers appreciated please as this is allowed under my schools rules. ...
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1answer
69 views

Score Statistic help!

Can someone help me with part B of this question please? I am completely stuck and do not know how to proceed. Hints rather than answers appreciated please as this is allowed under my schools rules ...
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1answer
23 views

How to find the asymptotic distribution of an estimator given the mean and variance of an estimator

I understand that the Delta Method can be used to find asymptotic distribution of estimators. I have a MLE Estimator with $ E[\hat\Theta] = \frac{n\Theta_0}{n+1} $ $ Var[\hat\Theta] = \frac{\Theta^...
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17 views

R codes: ecdf and kernel for standard normal distribution [closed]

I am studying about standard normal distribution. I have learned what is the pdf, cdf and the inverse of the cdf. I need help with R codes for empirical and kernel for the standard normal dis. ...
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17 views

Understanding weighting class estimator

What I understand is that in this scenario, the data is partitioned into Z weighting classes on the basis of variables observed for respondents and nonrespondents. $n_z$ represents the sample size, $...
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30 views

Basic hypothesis testing homework question

Suppose that random variable $X$ has the probability density function $$f_X(x)=\sqrt{\frac{\theta}{\pi x}}\exp(-x\theta), \quad x>0,$$ where $\theta$ is a positive parameter. It can be shown that $...
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1answer
23 views

probability sampling calculating probabilities

Consider a population with 10 elements , N:{0,1,2,3,4,5,6,7,8,9}. The probability of drawing ...
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1answer
32 views

Bayesian Homework: Uniform Prior

Suppose posterior density of parameter $\theta$ is $$\pi(\theta|\mathbf x)=\frac{\Gamma(5)}{\Gamma(3)\Gamma(2)}\theta^{3-1}(1-\theta)^{2-1}.$$ Now I have to find which of the two hypotheses $H_1:\...
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25 views

Bayes factor homework question

Suppose my $H_0:\theta=\frac{1}{2}$ Vs $H_1:\theta>\frac{1}{2}$. I got Bayes factor $$B_{01}(x)=\frac{f(\mathbf x|\theta_0)}{\int_{\Theta_1}f(\mathbf x|\theta)\pi_1(\theta)d\theta}=0.35.$$ From ...
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14 views

set of tasks from discrete financial market models

I'm looking for some books with tasks from discrete financial market models. What do you recommend? Preferably solved but not necessarily.
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1answer
38 views

How to vectorize Multivariate Gaussian distribution?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows: $p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/...
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53 views

positive correlation but p value is 0.152 [closed]

I have a positive correlation but my p-value is 0.152 am I being stupid or can any help it's kinda urgent
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33 views

$\mathbb{E}(W_1N_1(W_2N_2)^2)+\mathbb{P}(N_4>N_3>2, W_2<W_3<2)=?$

$W$ - Wiener process, $N$- Poisson Process with parameter $\lambda$ and $W$ and $N$ are independent. Compute: $\mathbb{E}(W_1N_1(W_2N_2)^2)+\mathbb{P}(N_4>N_3>2, W_2<W_3<2).$ $\mathbb{E}(...
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17 views

statistic significance of proportions

Let's assume someone buys a bag of smarties, and finds that it includes 22 brown candies 19 red candies 16 yellow candies 15 blue candies 8 green candies How can we use a test of significance to ...
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12 views

Is $B_t= \begin{cases} tW_{\frac{1}{t}}, t>0 \\ 0, t=0 \end{cases} $ a Wiener process? [closed]

Hi I need to check if $B_t= \begin{cases} tW_{\frac{1}{t}}, t>0 \\ 0, t=0 \end{cases} $ is a wiener process or not where $W_t$ - wiener process.
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24 views

find the distribution of random variable (Wiener process)

$X_t=(t+3)W_{t+2}-2W_t$, $t>0$, $W_t$- Wiener process. I have to find the distribution of a random variable $X_t$ and answer the question whether it is a Wiener process. How to determine this ...
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41 views

Likelihood of a single sample being in one of two populations

Consider the following analogy: I observe a man who is 175 cm tall. Independent of height, there is an equal chance that he could be from either Country A, or Country B. The height of men in Country ...
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28 views

Let {et } be a zero mean white noise process. Suppose that the observed process is Yt = et + θet _ 1, where θ is either 3 or 1/3. )

I am supposed to find the autocorrelation functions for the respective values of theta. From what i've read from the textbook, i should take place the covariance of Yt and the lag of Yt in the ...
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1answer
18 views

Conditional Probability Problem Computation / Setup Check

I am looking for some help or validation of setup of a conditional probability problem. The details and the way I went about it are below! Conditional Probability Givens: P(First) = guerillas ...
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24 views

Confirming meaning of Random Variable [closed]

Following several detailed posts on the topic of Random Variables What is meant by a “random variable”? Clarification - Random Variable Independent variable = Random variable? I would like to ask a ...
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16 views

Stochastic transition matrix clarification

I am studying stochastic processes, and I don't quite understand what does it mean to go from state $i$ to state $j$ in two steps. As given in the definition and properties page on wikipedia , if ...
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26 views

Explainability of a model

I am trying to answer this question: This question is actually based on the Mackay plot here: the simpler the model, the more it places its mass towards the left However I'm not quite able to arrive ...
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36 views

Vector Autoregressive Models (VAR) and error terms correlation

Before all I want to clarify, I am not looking for a direct answer in the following question but more of a clarification. I am doing a master's degree and the question is part of an assignment, so i ...
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22 views

Clarifying the meaning of i.i.d. when describing a set of variables

Let $Z_1, ..., Z_k$ be identically and independently distributed (i.i.d.) set of standard normal random variables. I understand that as part of the i.i.d. independent broadly means that variables ...
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38 views

Small noise of state process and filtering

Assume we have a linear state-space model: $$ z_{k} = Hx_{k} + v_{k}\\ x_{k} = F x_{k-1}+ w_{k}. $$ We are interested in filtering, i.e. we aim to estimate $E[x_{n}|z_{0}, \dots, z_{n}]$. If the ...
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1answer
58 views

Random walk based on coin toss [closed]

You are in an open field with two coins and you alternate flipping the coins and taking steps by the following rules: ...
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0answers
46 views

Is my statistical model correct?

I have to construct a statistical model for the random variable $X=(X_1,X_2) \sim N(\mu+\alpha_1,1) \times N(\mu +\alpha_2,1), \mu \in \Bbb R, \alpha_i \in \Bbb R$ and tell if it's identifiable. What ...
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35 views

Equality of estimators Yule walker and Least squares AR(m)

I prepare for my exams from Time Series and I try to do some proofs on my own. Here is my last problem. I would like to see any tips from you. Let $X=\{ X_t: t \in \mathbb{Z}\}$ be $AR(m)$ causal ...
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13 views

Suggesting the Most Powerful test based on NP lemma- Bernoullie distribution

A country that gives the UK points in the Eurovision Song Contest with a probability of $p=0.5$ would be called "a UK supporter", whereas a country that gives the UK points with a low probability of $...
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26 views

Average number of trials required to get 13 successes in a row, assuming a success rate of 70%

If, for example, I toss a weighted coin (with a 70% chance of getting heads), how many flips would be needed on average to get a run of 13 heads in a row?
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1answer
55 views

Find the CDF and use it to find all the medians

Show that for every $p$, $0\leq p\leq 1$, the function $f(x)$ = $p*sin(x) +(1-p)*cos(x)$, $0\leq x \leq \pi/2 $, and $f(x)=0$ otherwise, is a density function. Find its CDF and use it to find all the ...
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1answer
30 views

Transformation of Uniform(0,1) random variable [closed]

Let $X \sim U[0,1]$. Find the pdf of $Y=4\sqrt{X}(1-\sqrt{X})$. I have been studying transformation of random variables and came across this exercise. Can anyone provide me a hint on how to ...
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0answers
35 views

Prove that Z = X + Y is a Poisson random variable; X|X + Y is a Binomial random variable [closed]

Let X be a Poisson random variable with parameter λ and Y be a Poisson random variable with parameter μ; X and Y are assumed to be independent. a) Prove that Z = X + Y is a Poisson random variable ...
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54 views

Show that $E[u(X_1)\mid\sum^n_{i=1}X_i=z]=\Phi \left( \frac{\sqrt n(c-z/n)}{\sqrt{n-1}} \right)$ [duplicate]

Let $X_1, ..., X_n$ be a random sample from the $N(\mu,1)$ distribution. First show that $$E \left[ u(X_1)\, \Big|\, \sum^n_{i=1}X_i=z \right] = \Phi \left( \frac{\sqrt n(c-z/n)}{\sqrt{n-1}} \right)\,,...
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10 views

Maximum likelihood estimator for difference of parameters

We're comparing two different clinical treatments. For each patient we observe the pair $(Y_i,R_i)$, where $Y_i$ denotes if the treatment was successful ($Y_i=1$) or not ($Y_i=0$) and $R_i$ indicates ...
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1answer
32 views

Calculating probability given mean and variance without using z-score

i need to calculate the probability $P(X<-0.03)$ with $E(X)=0.01$ and $Var(X)=0.04$ without knowing the distribution. Only thing I know is that $X$ is symmetrically and continously distributed. I ...
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1answer
38 views

Is $P(X+2 = x+2)$ the same as $P(X=x)$?

I'm trying to derive $E[X+c]$ and show that this equal $E[X] + c$ (where $c$ is a constant), however my logic relies on the above being true. If anything has an alternative proof that would be very ...
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1answer
91 views

Most powerful test for simple hypothesis for $N(0,\sigma^2)$

Let $X_1,X_2,...,X_n$ denote a random sample from density, $N(0,\sigma^2)$, Find the most powerful test for testing the simple hypothesis $H_0:\sigma= \sigma_0^2$ vs $H_1:\sigma=\sigma_1^2$ where $\...
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1answer
39 views

Determining which variable is the cause and which one is the effect

I'm working on my assignment and I'm a bit lost. So the assignment requires us to draw a scatter plot based on data that we collected online. The purpose of the assignment is to see if higher earnings ...
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1answer
39 views

How to calculate the distributed of samples come from Gaussian distribution?

The question says, if $x_1$ and $x_2$ are samples come from a same Guassian distribution $N(0, \sigma^2)$, prove that Statistics $x_1/x_2$ and $\sqrt{x_1^2 + x_2^2}$ are independent. I'm really ...
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0answers
16 views

Request for Explanation: Deriving Probability Density Function of a Maximum Likelihood Estimator of a Uniform Distribution [duplicate]

I am reviewing some practice problems and have both a question and its solution but am struggling to understand them and am hoping someone can help me. I am struggling to follow the logic for ...
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1answer
16 views

Are these latent variables too highly correlated in this Structural Equation Model?

this is my first SEM I've done so I'm still getting my head around many of the concepts. So I think I've created a hierarchical model of IQ (generaliq), with the latent variables: verbal_letter, ...
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1answer
36 views

Random Walk or Gambler's Ruin

I am doing a practice problem in chapter 3 (problem 81) in my old probability book "A First Course in Probability" by Sheldon Ross, 5th Edition. Most of the problems have answers so I can check my ...
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1answer
19 views

How to interpret correctly this chart about nitrogen oxide?

I found the below chart in a test for university access in Sweden, with the following question: How large was the total emission of nitrogen oxides caused by Swedish consumption under the period 2004-...
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0answers
54 views

What is the laplace transform of the below given PDF?

Really am interesting to know more about statistical properties of the following PDF , of the Random variable $z$: $$F(\sigma,\mu,z)= \frac{(z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2 \sqrt{\left(...
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0answers
19 views

Deriving the $p$-dimensional maximum likeliihood estimation

So I'm currently following a statistic course and we are deriving the maksimum likelihood estimator for a $n\times p$-dimensional normal disitribution. So for $\mathbf{X}=\begin{pmatrix} \mathbf{X}_1^*...
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53 views

Is this the correct way of working on an ML problem?

I am working on an assignment where I have been provided a data-set using which I have to do the following: A. The data in the F20 column is missing, I have to use various imputation strategies and ...
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46 views

Range of values of $R^2$ for a two-feature linear model based on the $R^2$s of one-feature linear models?

I was asked this in an interview. You have two features, $x_1$ and $x_2$. You fit a simple linear model on each feature, so $$ \underbrace{y = x_1 \beta}_{\text{model 1}}, \qquad \underbrace{y = x_2 \...
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1answer
26 views

Patient, Doctor and flu vaccination [closed]

The Department of Health encourages young children to have a flu vaccination each year. The vaccination reduces the likelihood of getting a flu from 40% to 10%. If 45% of the young children visiting ...
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0answers
37 views

Why is ABC interaction completely confounded in this factorial experiment?

Consider a 2^3 factorial design layed out in 2 blocks ,with plot size 4, as follows Block I: {1,ab,ac,bc} Block II: {a,b,c,abc} This is replicated four times. abc is said to be completely ...