The reflection principle says that for the Markov process $(B_t,\mathcal{F}_t,P_x)$ associated with Brownian Motion it is satisfied that $P_0(\text{max}_{...

I have the following problem: The expectation of an exponentially distributed random variable $X$ is equals to $1/2$. Compute $\mathbb{E}[e^{-2x}]$. The f...

I'd like to cut the $3$-sphere of radius $1$ with the plane $x+y+z=k$. Of course the cross-section is a circle: the problem is that I'd like to ...

According to Wikipedia, a harmonic function is one which satisfies: $$ \nabla^2 f = 0 $$ The spherical harmonics (also according to Wikipedia) satisfy the...

Is every subgroup of a normal subgroup normal ? That is if $H$ is a normal subgroup of a group $G$ and $K$ is a subgroup of $H$, then $K$ is a normal subg...

The following attempt of mine at defining these terms, reflects my current understanding of them: Assumption: $\quad$ A statement accepted as true without...

I am working on getting the hang of proofs by induction, and I was hoping the community could give me feedback on how to format a proof of this nature: Le...

Is showing that $f_{xy}$ is not equal to $f_{yx}$ at a given point sufficient/good to show that a function is discontinuous there? Can you also suggest a ...

Let me start of by specifying the question: A and B are two towns. Kim covers the distance from A to B on a scooter at 17Km/hr and returns to A on a bicyc...

So I was given the equation below and was told to solve for x. $$\sqrt3\cos(x) - \sin(x) = 0,x \in [-\pi, \pi] $$ Naturally I rearranged the equation to b...