$X_1$ be an exponential random variable with mean $1$ and $X_2$ be a gamma random variable with mean $1$ and variance $2$ find $P(X_1

Help me prove: sin(A+B) = sinA cosB + cosA sinB [duplicate]

Can you help me prove that: sin(A+B) = sinA cosB + cosA sinB? Thanks!

How to solve $(A-AX)^{-1}=X^{-1}B$ and prove $B$ is invertible?

So this is a homework problem. So I'll give what I got. Suppose $A,$ $\ B$ & $X$ are $n$ by $n$ matrices with $A,$ $\ X$ & $A-AX$ invertible....

If $Var(X)=0$ then is $X$ a constant?

We know that the variance of a constant is $0$. Is the converse also true? Can we say that if the variance of some random variable is $0$ it is a constant?

How to show a subset is part of another set?

I'm not sure how to "show" these two answers. The small group created from the intersection $A\cap B\cap C$ is a subset of $A\cap B$ since abc is a s...

Proof of logarithm power change

I am not too sure how to explain this in words. So the question is proofing that $a ^{\log_bc} = c ^{\log_b a}$ So far what I have done was: I cannot thin...

Derivative vs division

Suppose we have a function $s=16t^2$ now if we find $\frac{ds}{dt}$ we get $v=28t$ but when we simply divide we know $s/t=v$ so $s/t=16t$. Why classical d...

characteristic of a finite field

knowing that the characteristic of an integral domain is $0$ or a prime number, i want to prove that the characteristic of a finite field $F_n$ is a prime...

What is the best Classical Mechanics book for undergraduate?

I want to know which book is the best for undergraduate classical mechanics, given that I am well equipped with newtonian mechanics (From: University Phys...

Prove that for one vertex of a convex pentagon, the sum of distances to the other four is greater than the perimeter

The problem is from the journal 'Crux Mathematicorum', originally proposed by Paul Erdős and Esther Szekeres for the case of a convex $n$-gon wi...