# 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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### Finding the characteristic function of a simple linear PDF

X is a random variable with a pdf of $f(x) = \begin{cases} x/2, & 0 \le x \le 2 \\ 0, & \text{otherwise} \end{cases}$ I tried finding the characteristic function of this but ended up with ...
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### How do I find the probability of interference of a shaft and a bearing given their nominal diameter values and their standard deviations?

The exact question is as follows: An assembling of shaft and bearing is made out of shaft manufactured to a specification of 30.00 ± 0.09 mm and bearings are manufactured to a specification of 30.10 ±...
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### Why should we study copulas? [closed]

I am new to the study of copulas and I would like that someone could provide some examples where they are applied, their usefulness and so on. Any help is appreciated. Thanks in advance.
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### What receptive field do we have after stacking $n \times n$ CONV layers with kernel size $k \times k$?

What receptive field do we have after stacking $n \times n$ convolutional layers with kernel size $k \times k$ and stride $1$? Layers numeration starts with $1$. The resulting receptive field will be ...
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### Rao-Blackwell for Minimum-Variance Unbiased Estimator

Let $X$ be an observation from a distribution with probability mass function:$f(x;\theta) = \left(\frac{\theta}{2}\right)^{|x|}(1-\theta)^{1-|x|}I_{\{-1,0,1\}}(x), \, \theta \in (0,1).$ Use Rao-...
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### Literature / Books on Linear Models, Generalized Linear Models and Linear Mixed Models

As the title suggests, I'm looking for book recommendations on Linear Models, Generalized Linear Models and Linear Mixed Models. The book should give a good overview on the intuition behind ...
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The question is pretty much in the title, I need to find an approximate distribution of $XY$ when $(X,Y)$ follow a Bivariate Normal Distribution where $X$ and $Y$ are each $N(0,1)$ distributed and $... 0answers 9 views ### F test, Model selection test How to compare which of the following two models is a better fit: M1$y$=$\alpha$$X + \epsilon M2 ln(y) = \alpha$$X$+$\epsilon$Can we run a test statistic to compare the two models? ... 0answers 30 views ### Maximum likelihood estimation versus a given interval I have been solving some exercises on Maximum Likelihood estimation and I got across this one- It is known that the proportion of smokers (p) in a population lies in the interval$[1/3, 2/3]$. In a ... 0answers 21 views ### Self-study: Which option is NOT a prediction of the central limit theorem? "All of the following are predictions of the Central Limit Theorem except: 1) The sample mean distribution will be approximately normally distributed if the sample size is large 2) The mean of the ... 1answer 78 views ### Distribution of sums and differences of n correlated normal random variables Suppose$x_1\sim\mathcal N(2,0.5),x_2\sim \mathcal N(2,3),$and$x_3\sim \mathcal N(2.5,7)$with correlations$\rho_{(1,2)}=0.3,\rho_{(1,3)}=0.1,$and$\rho_{(2,3)}=0.4.$What is the distribution of ... 1answer 47 views ### Approximate distribution for sum of squares of standardized Poisson random variables Suppose that$X_1, ..., X_n$are independent and identically distributed Poisson($\lambda$) random variables. What is a good approximating distribution for$\sum_{i = 1}^{200} \frac{(X_i - \lambda)^2}...
Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $\mu_1$ and unknown variance $\sigma_1^2$. A second random sample from another ...
I am stuck on the following question and I was wondering if can get some help. Let $f(x;\theta) = g(\theta)h(x),\ a(\theta) \leqslant x \leqslant b(\theta)$ with $a(\theta)$ decreases and $b(\theta)$...