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monotone class theorem, proof
I am having difficulty with this proof: It is the three sentences I have colored that is very difficult. Could someone please explain why they are true? r...
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Calculation of inverse of chi-square's expectation
I don't know where to begin to calculate the expectation value of the random variable $1/V$, where $V$ is a random variable with chi-square distribut...
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How to convert octal to decimal?
I tried to convert octal numbers to decimal numbers and I found the formula but I am expecting a different way. My way is: the octal is $547$. Formula: $(...
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Examples of functions that are not functionals
Functionals are known as functions that give a number as an output. Are there examples of functions that do not give a number as an output? I find it stra...
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Matrix and vector multiplication in component notation
I am confused about the index notation when it comes to matrix and vector multiplication. Let $A,B\in GL(n,\mathbb{R}), x\in \mathbb{R}^{n}$. I know that ...
Read Journal![Why is A intersection A' null? [closed]](https://ly.shilpakalanarail.gov.bd/uploads/why-is-a-intersection-a-039-null-closed_720.jpg)
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Why is A intersection A' null? [closed]
Intersection between 2 sets means the elements that are common to both those sets. I read that at Wikipedia. $\varnothing$ is the subset of every set but ...
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How exactly does one define the "spectral measure" of an operator?
I am seeing kind of different definitions of "spectral measure" at different places and its not clear to me as to what is the universal idea. It would be ...
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Find the center and radius of a sphere
Find the center and radius of a sphere that has $(1,-2,4)$ and $(3,4,-12)$ as endpoints of a diameter. Okay. I Understand how to find radius. It is merely...
Read Journal![TI 89 vs TI 84 Plus CE [closed]](https://ly.shilpakalanarail.gov.bd/uploads/ti-89-vs-ti-84-plus-ce-closed_720.jpg)
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TI 89 vs TI 84 Plus CE [closed]
I am currently a sophomore in high school taking Algebra 2 and Precalculus in the same year. Junior year I’ll be taking AP BC Calculus and then Senior yea...
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Probability of a Rubik's Cube being solvable in two moves.
So, I have recently gotten into speed-cubing, and I ran into a very interesting problem. According to the World Cube Association, a cube is legal if it ta...
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