# Questions tagged [self-learning]

The process of studying mathematics without formal instruction. Don't use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is about.

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I am a sophomore math major. Because of being in a bad University I am deprived of good math instruction and peer group which has left me alone to pursue this subject. At first, I used platforms like ...
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### Monte Carlo Control Reinforcement Learning

I'm reading the "Reinforcement Learning" book by Sutton & Barto. It's available here http://incompleteideas.net/book/RLbook2020.pdf . I'm currently in chapter 5 on Monte Carlo methods. I ...
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### Density of sum of two random variables

Let$(X,Y)$ be an RV of the continous type with PDF $f(x,y)$.Let $Z=X+Y$,then the Convolution of probability distributions told us the PDF of $Z$ is $f_{Z}(z)=\int_{-\infty}^{\infty}f(x,z-x)dx$. If we ...
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### Find the distribution of $X|Y=y$ where X and Y look like a a bivariate poisson.

It isn't a bivariate Poisson precisely, but has a pmf of: $$\mathbb{P}(X=x, Y=y)=\frac{\lambda^y e^{-2 \lambda}}{x !(y-x) !} I_{\{0, \ldots, y\}}(x) I_{\mathbb{N}}(y), \lambda>0$$ When I tried to ...
Let $X$ and $\mu$ are $p$ dimensional vector and $\Sigma$ $p\times p$ dimensional matrix. I have to simplify the following expression. $-\frac{1}{2}(X-\mu)^T\Sigma^{-1}(X-\mu)$ $=-\frac{1}{2}(X^T-\mu^... • 113 0 votes 2 answers 111 views ### Simple question regarding the Poisson distribution I'm just trying to wrap my head around the Poisson distribution to make it more intuitive and I'm struggling with one (seemingly) paradoxical example. Say we have a rate of 4 events in a given time ... 0 votes 0 answers 36 views ### Is it possible to study Measure Theory from the definition of Measure? I would like to start studying Measure Theory in the summer of 2024. Let me tell you a bit about myself: I'm a graduate student in Mathematics from Brazil. I suspect that, by luck, I ended up being ... 2 votes 0 answers 58 views ### References for Exercises on Abstract Simplicial Complexes I am currently reading Combinatorial Algebraic Topology by Kozlov. I'm enjoying it a lot, however, it regretfully does not contain any exercises (it is more along the lines of lecture notes). In the ... • 2,397 0 votes 1 answer 53 views ### Intuitive online resources/books for statistics? (Sorry for any spelling/grammatical mistake. I am from South America.) This semester I took my first Statistics course in college, and I feel that ever since the concept of the$T$distribution was ... • 31 0 votes 0 answers 13 views ### Please Explain why we take the product of two variables in a rate model (or any model)? I'm trying to understand this equation: v = k[A][B] where v is the rate of a chemical reaction, k is the rate constant, and A and B are reactant concentrations. I think this equation relates reaction ... • 1 1 vote 0 answers 116 views ### Problem on convergence in distribution of a random vector The issue is that I have to prove the following with limited resources. Problem: Let$X_n$and$Y_n$be p-dimensional random vectors. Show that if$X_n − Y_n \xrightarrow{P} 0$and$X_n \xrightarrow{D}...
I was asking myself this question. We define for an exact vector field $\mathbf{v}(\mathbf x) \in \mathbb{R}^n$, s.t. $\mathbf{v}(\mathbf x)=\nabla u(\mathbf x)$ for a potential $u$, a solution as a ...