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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 \...