# 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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### efficiency of estimator, $\bar (\frac{1}{X^2})$ vs $\frac{1}{\bar X^2}$ vs $\frac{1}{\bar (X^2)}$

I was studying point estimator, and I tried to compare the variances of the estimators to find out which one is more efficient. (Hogg, Tanis "Probability and Statistical Inference" Ch.6) It ...
1 vote
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### For a set of n Exponential iid RV, what is the probability that the maximum exceeds the sum of the others?

My question stems from self-study of question 91 in page 372 of Ross's Introduction to probability models, 12th edition. The answer is given in the textbook but I am trying to understand a specific ...
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### Proof of convergence of random variables in $L^p$ via convergence in probability and uniform integrability.

Consider the following proposition. Part (i) i have no problem with. Its the proof of part (ii) that (because of my lack of knowledge of advanced measure theory) am having trouble in understanding. ...
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### How to know what to study based on past examinations?

TL;DR: Tell me which topics should i study the most, based on this three tests: Mathematics (A): 2020 2019 2018 This question may sound a bit weird, since the natural answer would be "study ...
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### best textbooks for difficult specialist maths questions in year 11

I am currently studying year 11 specialist maths in Western Australia and I am doing the O.T. Lee textbook, however, I am looking for harder questions that will properly challenge my conceptual ...
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### Miscellaneous questions about Lebesgue measurable set and Lebesgue measure [closed]

(Definition of Lebesgue measurable set and measure) If a set $\mathcal{M}$ and a measure $\mu$ satisfy i) $\mathcal{M} \supset \mathcal{B}(\mathbb{R}^n)$, ii) any rectangle subset of $\mathbb{R}^n$ ...
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### Turning a pole/ladder horizontally at a corner

I've been attempting to solve the following problem: A lane runs perpendicular to a road 64 ft wide. If it is just possible to carry a pole 125 ft long from the road into the lane, keeping it ...
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### Obscure Results and Areas of Mathematics

My degree is in economics although I did relevant mathematics in college and used algebraic topology in my thesis. Over the Pandemic I've been reading a lot of mathematics that I didn't get a chance ...
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### Calibrating a Discrete Autoregressive Model using the Method of Moments

Consider the following discrete autoregressive $\epsilon_t$, where $\epsilon_t \in (\pm 1 ) \forall \ t \geq 1$. We think of $\epsilon_t$ as the child of a previous sign at time $t-l$, where $l$ is ...
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### Does this proof of the Boundedness Theorem contain a mistake?

My course notes (mathematics BSc, second-year module in real analysis, unpublished) have a proof of the Boundedness Theorem which begins: But does that sequence work? Here's my reasoning. Let \begin{...
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### A good book on topology for self-study

What's a good book for self-study on a first topology course? I'm taking topology for the first time, and my professor isn't what you might call great, everything is utterly easy or trivial for him, ...
1 vote