# 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.

5,859 questions
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### How do we compute OLS coefficients from Sum of Squares in multiple linear regression?

Suppose we have a variable y which is dependent on 2 variables say x1 and x2. Then I can understand how we can compute Sum of squares due to x1 and x2. For instance we may have Type I Sum of squares ...
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### Plot the exact density of a transformation of a distribution

I would like to compute (and plot) the exact density of the following distribution: $X_i \sim exp(-Exponential(\lambda)) - 0.5$ I already have the estimated density for this distribution, but I ...
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### Newsvendor problem with Poisson demand

Problem: The demand for a particular weekly magazine in a newsstand follows a Poisson distribution averaging 5.2 copies per week. The value paid for each magazine is 15.00 and the sale price is 30.00....
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### Is a Kalman filter ever the optimal way to estimate a dynamic value given a full history of measurements?

I'm trying to get some intuition for Kalman filtering, and I conceived this toy example: Say that I have a sensor that tracks a moving 1-dimensional target. Say that the measurements from the sensor ...
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### Is the likelihood in Bayes theorem a probability? [duplicate]

First some notation and definitions: In the Bayes formula as written for machine learning applications, $$p(\theta|D) = \frac{ p(D|\theta) p(\theta) }{ p(D) }$$ commonly $p(\theta)$ is labeled ...
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### EM Algorithm for Bayesian Networks with missing data

Setting: learning parameters of Bayesian Network (BN) with missing data. Algorithm: Expectation-Maximization. Question: suppose I am in the M-step, and that in the complete data there are no ...
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### How to determine the line which a time-series fluctuating around

Let $X_t=1+3t+0.5X_{t-1}+ \epsilon_t$ be a trend-stationary model, where $\epsilon$ is a white noise, which has zero expected value and standard deviation. Which line is the time series fluctuating ...
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### Residual Sum of Squares degrees of freedom intuition [duplicate]

Let RSS = Residual sum of squares $= \sum (y_i - \hat{y}_i)^2$. Without proof, $\frac{RSS}{\sigma^2} \sim \chi^2_{n-2}$. I do not quite understand why the DoF is $n-2.$ Could someone explain?
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### What is the probability that the new commitment will be fulfilled?

A consulting firm was hired to develop an Engineering project. Based on their previous experience, the direction of this office knows that the time (in months) needed to perform this type of task ...
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### Calculate a confidence interval of 88% for the difference in proportions [duplicate]

A survey of 400 men and 400 women in a certain city showed that 270 men and 240 women favor a certain proposition. Calculate a confidence interval of 88% for the difference in proportions between men ...
Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding. The first is Consider$$f(x|\theta)=h(x)\... 0answers 27 views ### Calculate R^2, R^2_{adj}, and F-statistic from \text{R} model summary I am given the full model, M_{\tt f}, with the regression line$$ {\tt response} = \beta_0 + \beta_1{\tt A} + \beta_2{\tt B} + \beta_2{\tt C} + \beta_4{\tt D} + \beta_5{\tt E} + \beta_6{\tt F} + ...
I am trying to calculate $F_Y(x)$ (CDF) of $Y=X^2$ where $X$ is a random variable of Laplace Distribution $f_X(x) = \frac{1}{2}e^{-|x|}$ (let's take a simple case when parameters $\mu=0$ and $b=1$). ...