# Tagged Questions

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_.

40 views

### Calculus: Differentiable Function and Tangent Line

I am not sure how to approach this question: Let $f(x)$ be a continuous and differentiable function of order 2. Let $f ''(x)>0$ for all values of $x$. The tangent line to the function at $x=1$ ...
76 views

I'm self learning and I stumbled upon the following exercise but I'm not sure if I solved it correct as I'm very new to this. Problem: 7 balls fall independently into 7 baskets. Let $X_i$ = number of ...
47 views

### Probability with coins

I'm self learning and I stumbled upon the following task, but I struggle to find the solution: Two players flip coins. The first player flips 3 coins, the second player flips 2 coins. The player that ...
37 views

### Probability Question - Paper Notes in a bag

I could do with some help with this question. In a bag there are 18 paper notes. On five of them there is the digit 2, on seven the digit 3, and on six the digit 5. A man takes 3 notes by random. If ...
71 views

### Probability: breaking keyboard

I'm trying to self-learn theory of probability, I came across the following basic problem that I think I solved but I'm not sure as I'm very new to this. Problem: A keyboard manufacturer states that ...
64 views

### To prove $\sup B \leq \sup A$

Assume $A$ and $B$ are non empty and bounded above and satisfy $B \subseteq A$. Show that $\sup B \leq \sup A$ I am thinking of proving using contradiction, but I am getting nowhere. Someone please ...
46 views

### To show that $\sup B=\inf A$

How do i show that To show that $\sup B=\inf A$ , where $A$ is set bounded below and B ={$b \in R$ : $b$ is a lower bound for $A$} Let $x=\sup B$ and $l=\inf A$. Now All lower bounds of A are less ...
22 views

### Showing weak law of large numbers holds

My question: $\{X_n\}$ is a sequence of random variables. Var$(X_n)\le C\ \ \forall \ n$ and $\rho_{ij}=$Cov$(X_i,X_j)\to 0$ as $|i-j|\to \infty$ . Show WLLN holds. In my book there are 3 ...
69 views

### Self Study of number theory

I have always wanted to learn about number theory. There is actually no one here who can teach me and it's also not in my regular school syllabus, but the greatness of number theory attracts me ...
43 views

### Proof for functions of matrix [closed]

Let $A \in \text{Mat} (n,n,\mathbb{C})$. Let $I$ be a subset of $\mathbb{R}$ or $\mathbb{C}$. Further, let $f:I\to\mathbb{C}$ and $g:I\to\mathbb{C}$ be two functions for which $f(A)$ and $g(A)$ are ...
23 views

### Composition of substitutions of SLD tree

I found a question on my university past paper and it asked to get the SLD tree from a computation rule using some rules and facts. However I obtained the answer and to complete the question I have to ...
99 views

### Finding total number of multi-sets

I am provided with a multi-set, let's say S with elements as [num1, num2, num3] and these elements are integers (both negative as well as non negative). As this is a multi-set, elements in the multi-...
40 views

### Joint pdf of X and Y with absolute value

Question. Joint probability function of continuous probability X, Y is here : $f_{X,Y}(x,y) = k(|x|-|y|) \ \ \ \ \ \ \ \ \ \ (-1< y< x< 2)$ Then what is k? I mean how can I differentiate ...
48 views

63 views

### Rigorous Approach to Precalculus

I've made the mistake of looking at more advanced texts that deal with precalculus-level mathematics in a more formal, rigorous way than usual. Perhaps this isn't a mistake, but now that I've glimpsed ...
2k views

### Why is a square root not a linear transformation?

The question says: Prove that the function $f(x)=\sqrt{x}$ is not a linear transformation (particularly $\sqrt{1+x^2}≠1+x$) I think that this is because the exponent of $\sqrt{x}$ is $1/2$, ...
30 views

### Prove identity by induction

Recently I read in lecture notes that for $\alpha \in \mathbb{N}^m$ with $\vert\alpha\vert = r$ the following identity holds: $$\sum_{} \frac{1}{\alpha!} = \frac{m^r}{r!}.$$ Appearently one can ...
14 views

### Linear Programming - Constraints

I am trying to encode this (a small part of a project that I am trying to do by self-learning) to linear programming: For each package p we know its length (xDimp) and width (yDimp). Also, we have ...
185 views

### Learning differential calculus through infinitesimals

In class, we've studied differential calculus and integral calculus through limits. We reconstructed the concepts from scratch beginning by the definition of limits, licit operations, derivatives and ...
20 views

### Explain the use of Dominated Convergence Theorem

In the proposition below from Measure Theory and Probability by Athreya and Lahiri, DCT was used to justify the existence of $t$ in the first line of the proof. But I can't think how this was ...
52 views

16 views

### How to compare two tests according to the power of the test?

enter image description here Can the rejection region calculated from the problem? I'm a little bit confused by all this staff.
24 views

### How many people did the test at most?

There are 3 questions in a test and the full mark of each question is 7. Each question can only be marked with integers: $1, 2, 3, \cdots, 7$. We know that the product of everyone's marks of the 3 ...
27 views

### Derivative notation question

$d = \frac{(u+au)^2}{\frac{u^2}{r} + \frac{(au)^2}{s}}$ I have a basic question concerning derivatives. If I need to find the max of $d(a)$, I know I need to take derivatives... but with respect to ...
25 views

### What should I be studying if I want to calculate correlation between data sets?

I'm building an app that brings in data from multiple API's (Stripe, Google Analytics, Github). I'd want to be able to analyze the different sets of data against each other if at all possible and draw ...
I want to prove that the limit of function $\displaystyle \lim_{x \to \infty}\frac{\ln(x)}{x} = 0$ Of course it is easy to find it by l'hopital's rule, but i want to find it using the power series ...