1,753 reputation
1523
bio website
location
age
visits member for 2 years, 11 months
seen 4 hours ago


5h
comment What does it really mean when we say that the probability of something is zero?
@krb686 - "How so?": The computable reals in any interval form a null set (i.e., whose Lebesgue measure is zero). This is a mathematical issue, not a physical one.
6h
comment Finding an expression for a joint probability if two random variables have the same distribution function.
@MathDamon - I've added that to the answer.
6h
revised Finding an expression for a joint probability if two random variables have the same distribution function.
add similar development for min(X,Y)
10h
comment What does it really mean when we say that the probability of something is zero?
Indeed, if X has a continuous distribution on a real interval then ℙ( "X is computable")=0.
10h
comment What does it really mean when we say that the probability of something is zero?
Or you can think like the Queen: "Alice laughed: "There's no use trying," she said; "one can't believe impossible things." "I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." $\sim$ Alice in Wonderland
11h
revised Finding an expression for a joint probability if two random variables have the same distribution function.
added 63 characters in body
11h
answered Finding an expression for a joint probability if two random variables have the same distribution function.
11h
comment Finding an expression for a joint probability if two random variables have the same distribution function.
Is it to be assumed that the distribution of $X$ is continuous?
11h
revised Use Random Number to Derive # based on Probability Table
edited body
11h
revised Use Random Number to Derive # based on Probability Table
added 1 character in body
11h
answered Use Random Number to Derive # based on Probability Table
2d
comment Is there a prime number ending with the natural number $n$
What do you mean? What follows from what very existence? (Note that there are two links in my previous comment.)
2d
comment Is there a prime number ending with the natural number $n$
For any positive integer $n$, there are infinitely many primes "beginning" with $n$, and if $n$ "ends" with $1,3,5$, or $7$ then there are infinitely many primes "ending" with $n$.
Sep
10
comment What does $d\mathbb{P}(\omega)$ in integral mean?
Wouldn't this be improved by including the definition and perhaps a link, e.g. to Lebesgue integration?
Sep
10
revised What is the correct equation for conditional relative entropy and why
"expected value" --> " expected value of the required form"
Sep
9
revised What is the correct equation for conditional relative entropy and why
add [entropy] tag
Sep
9
suggested suggested edit on What is the correct equation for conditional relative entropy and why
Sep
9
answered What is the correct equation for conditional relative entropy and why
Sep
7
comment Finite discrete approximation to the normal distribution
(cont'd) In fact, your "naive solution" is not symmetric, and yet does not exactly match an arbitrary mean. For example, with $\mu = 4.9, \sigma = 1$, and support $\{\lfloor \mu- 3 \sigma \rfloor, ..., \lceil \mu + 3 \sigma\rceil\}= \{1,...,8\}$, it gives $f(1)=0.0003369... \ne f(8)=0.004661...$ (not symmetric) and mean $=4.8998... \ne 4.9$ (not an exact match).
Sep
7
comment Finite discrete approximation to the normal distribution
Your requirements cannot be met for arbitrary mean $\mu$. This is because a symmetric approximating distribution with support $\{ a_1, ... a_n\} $ will have a mean that's necessarily either $a_{(n+1)/2}$ (odd $n$) or $\frac{1}{2}(a_{n/2} + a_{n/2 + 1})$ (even $n$); e.g., if the support is a set of consecutive integers, then the mean must be a multiple of $\frac{1}{2}$.