Intereting Posts

Is the composition function again in $L^2$
Show that $r$ is a spherical curve iff $(1/\kappa)^2+((1/\kappa)'(1/\tau))^2$ is a constant.
Intuition behind losing half a derivative via the trace operator
Infinite Set is Disjoint Union of Two Infinite Sets
Show that all abelian groups of order 21 and 35 are cyclic.
Approximation in Sobolev Spaces
When can we find holomorphic bijections between annuli?
Why is the Continuum Hypothesis (not) true?
$\int_0^\infty \frac{\log(1+x)}{x}e^{-\alpha x}dx$
$SL(3,\mathbb{C})$ acting on Complex Polynomials of $3$ variables of degree $2$
Master Theorem. How is $n\log n$ polynomially larger than $n^{\log_4 3}$
When not to treat dy/dx as a fraction in single-variable calculus?
A basic question on convergence in prob. and a.s. convergence
Showing $\frac{\sin x}{x}$ is NOT Lebesgue Integrable on $\mathbb{R}_{\ge 0}$
What groups are semidirect products of simple groups?

The Product of Two Gaussain Random Variables is not Gaussian distributed:

- Is the product of two Gaussian random variables also a Gaussian?
- Also Wolfram Mathworld
- So this is saying $X \sim N(\mu_1, \sigma_1^2)$, $Y \sim N(\mu_2, \sigma_2^2)$ then $XY \sim W$ where W is some other distribution, that is not Gaussian

But the product of two Gaussian PDFs is a Gaussian PDF:

- Calculate the product of two Gaussian PDF's
- Full Proof
- This tutorial which I am trying to understand Writes: $N(\mu_1, \sigma_1^2)\times N(\mu_2, \sigma_2^2) = N(\frac{\sigma_1^2 \mu_2 + \sigma_2^2 \mu_1}{\sigma_1^2 + \sigma_2^2},\frac{1}{\frac{1}{\sigma_1^2} + \frac{1}{\sigma_2^2}})$

What is going on here?

- Intuition, proof, one-sided group definition - Any set with Associativity, Left Identity, Left Inverse is a Group - Fraleigh p.49 4.38
- List of Local to Global principles
- Is this a counterexample to “continuous function…can be drawn without lifting” ? (Abbott P111 exm4.3.6)
- Seminorms and norms
- Geometrical interpretation of a group action of $SU_2$ on $\mathbb S^3$
- Explaining Newton Polygon in elementary way

What am I doing when I take take the product of two pdfs,

vs when I take the product of two variables from the pdfs?

When (what physical situation) is described by one,

and what by the other?

(I think a few real world examples would clear things up for me)

- Intuition: Power Set of Intersection/Union (Velleman P77 & Ex 2.3.10, 11)
- Find a symmetric random walk on $\mathbb{Z}$ that is transient.
- Eliminating Repeat Numbers from a Hat
- constructive counting math problem about checkers on a checkerboard
- Book suggestion for probability theory
- Categorical description of algebraic structures
- Modified gambler's ruin problem: quit when going bankruptcy or losing $k$ dollars in all
- Probability that 2 appears at an earlier position than any other even number in a permutation of 1-20
- Chance on winning by throwing a head on first toss.
- Identifying joint distribution

The product of the PDFs of two random variables $X$ and $Y$ will give the *joint* distribution of the vector-valued random variable $(X,Y)$ in the case that $X$ and $Y$ are independent. Therefore, if $X$ and $Y$ are normally distributed independent random variables, the product of their PDFs is **bivariate normal** with zero correlation.

On the other hand, even in the case that $X$ and $Y$ are IID standard normal random variables, their product is not itself normal, as the links you provide show. The product of $X$ and $Y$ is a *scalar-valued* random variable, not a vector-valued one as in the above case.

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- $x\in \{\{\{x\}\}\}$ or not?
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- Prove if $56x = 65y$ then $x + y$ is divisible by $11$
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- Brownian motion (Change of measure)
- Need help proving this integration
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- Extension of the Jacobi triple product identity