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General Q&A about all branches of theoretical and applied mathematics, including closely-adjacent sciences where the central question is about the math.

373 posts RSS
Activity Age Score Random
Filters (None)
28%
+0 −3
Besides guaranteeing 0 ≤ P(A ∩ B) ≤ 1, why can't Independence be defined as P(A ∩ B) = P(A) +,-, or ÷ P(B)?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
33%
+0 −2
What is "continuous" in Math?

3 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

terminology
40%
+0 −1
How to find constant equal to what in integration?

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

classical-mechanics integration
50%
+0 −0
Is $x=\int \int \ddot{x}\mathrm dx \mathrm dx$?

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by celtschk‭

multivariable-calculus
66%
+2 −0
Do these major triangle lines have names?

0 answers  ·  posted 3y ago by Peter Taylor‭

euclidean-geometry triangle plane-geometry nomenclature
50%
+0 −0
Prove that $\int \ddot{x}(t)\mathrm dt=v_0 + \frac{F_0}{m}t$

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by celtschk‭

classical-mechanics integration
77%
+5 −0
Finding the smallest Mersenne-number multiple of an odd integer

1 answer  ·  posted 3y ago by wizzwizz4‭  ·  last activity 3y ago by Peter Taylor‭

binary mersenne-numbers algorithm factoring
50%
+2 −2
How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by Wolgwang‭

intuition
50%
+0 −0
Book suggestion for Tensor Calculus (Differential geometry)

0 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

tensor-calculus book-suggestion
42%
+1 −2
In $w_{k + 1} - w_k = (\frac{1 - p}{p})^{exponent}(w_1 - w_0)$, why isn't exponent $k + 1$?

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by leovt‭

probability
25%
+0 −4
Why "only 1/10,000 men with wives they abuse subsequently murder them" ≠ P(A|G,M) & "50% of husbands who murder their wives abused them” ≠ P(G|A)?

0 answers  ·  posted 3y ago by DNB‭

probability
28%
+0 −3
How can I exploit symmetry to intuit P(A wins) + P(B wins) = 1, without performing algebra?

0 answers  ·  posted 3y ago by DNB‭

probability
40%
+0 −1
Scalar that varies across one or multiple scalar axes

0 answers  ·  posted 3y ago by deleted user

scalar
42%
+1 −2
How do mathematicians measure shape perimeters?

2 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

geometry
40%
+0 −1
How to vaticinate calculating $w_{k + 1} = w_1(1 + \dfrac{1- p}{p} + \dots + [\dfrac{1- p}{p}]^k)$ separately for $p = 1 - p$ and $p \neq 1 - p$?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
33%
+0 −2
How does P(Monty opens door 2) = P(Monty opens door 3), and $P(\text{get car}|M_2)P(M_2) = P(\text{get car}|M_3)P(M_3)$?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
40%
+0 −1
How to visualize multiplication in the Odds form of Bayes's Theorem?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
40%
+0 −1
How to visualize division in the Odds form of Bayes's Theorem?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
81%
+7 −0
When and how should the $Z_n^2$ statistic be used?

1 answer  ·  posted 4y ago by HDE 226868‭  ·  last activity 3y ago by HDE 226868‭

statistics
71%
+3 −0
What is a dummy variable (in an integral)?

1 answer  ·  posted 3y ago by deleted user  ·  edited 3y ago by JRN‭

calculus integration gamma-function beta-function
66%
+2 −0
Find $y=b\cos^3\theta$ and, $x=a\sin^3\theta$ from hypocycloid's formula

1 answer  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

calculus hypocycloid parametric-equation
42%
+1 −2
How to determine area of square using Calculus in Cartesian coodinate?

3 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by celtschk‭

calculus integration
60%
+1 −0
Prove $(\cos^3\theta+\sin^3\theta)^2= \cos^6\theta(1+\tan^3\theta)^2$

2 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by Peter Taylor‭

trigonometry
40%
+0 −1
What is the meaning of integration under integral sign?

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

calculus integration
37%
+1 −3
How can "information about the birth season" bring "at least one is a girl" closer to "a specific one is a girl"?

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by r~~‭

probability
42%
+1 −2
Intuitively, why would organisms — that after one minute, will either die, split into two, or stay the same, with equal probability — all die ultimately?

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by Peter Taylor‭

probability
45%
+3 −4
Why does “unless” mean “if not”?

2 answers  ·  posted 4y ago by PSTH‭  ·  edited 3y ago by Peter Taylor‭

logic
25%
+0 −4
In the Monty Hall problem, why can you just assume the contestant picked door 1? Why are you entitled to relabel the doors, or rewrite this solution with the door numbers permuted?

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by Moshi‭

probability
33%
+0 −2
If a 2nd test's independent from the 1st test, then why does $\frac{0.95}{0.05}$ figure twice in $\frac{P(D|T_1)}{P(D^C|T_1)}\frac{P(T_2|D,T_1)}{P(T_2|D^C,T_1)}$?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
33%
+0 −2
Why so many books on introduction or bridges to proofs for undergraduates?

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by r~~‭

logic
28%
+0 −3
How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
60%
+1 −0
differentiate under integral sign says something went wrong

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by celtschk‭

calculus multivariable-calculus differentiation integration improper-integral
50%
+0 −0
Solve $\int_0^{\dfrac{\pi}{6}} \sec^3 \theta \mathrm d\theta$

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

calculus integration definite-integrals
50%
+1 −1
Intuitively, why does A, B independent $\iff$ A, $B^C$ independent $\iff A^C, B^C$ independent?

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by JRN‭

probability
50%
+0 −0
How does $\lim\limits_{n \to \infty} \dfrac{p[s + (1 - s)c^n]}{p[ s + (1 - s)c^n] + (1 - p)[s + (1 - s)w^n]} = p?$

1 answer  ·  posted 3y ago by DNB‭  ·  last activity 3y ago by r~~‭

limits
28%
+0 −3
Intuitively, if you pick k out of n objects singly without replacement, why's the number of possible outcomes NOT $n(n-1) \dots [(n-(k - 1)]\color{red}{(n - k)}$?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
28%
+0 −3
In the Lost Boarding Pass Probability Problem, why couldn't Passengers 2-99 sit in Seats 1 or 100, before Passenger 100 boards?

0 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
50%
+0 −0
methodology of integration by parts ($e^{ax}\cos (bx+c)\mathrm dx$)

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by r~~‭

calculus integration definite-integrals
50%
+0 −0
How to derive some trigonometric formulas?

2 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

trigonometry
66%
+2 −0
$\sum_{k=0}^{n} \binom{n}{k}=2^{n} \overset{?}{\iff} \sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

combinatorics
60%
+1 −0
Find the intervals on which it is increasing and those on which it is decreasing of the following function.

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

calculus derivatives real-analysis functions maxima-minima
33%
+0 −2
Why isn't the probability of being void in 3 specifi c suits $\frac{1/13}{\dbinom{52}{13}}$?

0 answers  ·  posted 3y ago by DNB‭

probability
50%
+0 −0
How does the change of variable $\color{red}{r↦n−r}$ transmogrify $\sum\limits_{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits_{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by Moshi‭

summation
57%
+2 −1
Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio?

2 answers  ·  posted 4y ago by Chgg Clou‭  ·  last activity 3y ago by celtschk‭

probability
50%
+0 −0
Differentiating a series expansion of an arbitrary function

1 answer  ·  posted 3y ago by deleted user  ·  edited 3y ago by Mithrandir24601‭

calculus derivatives differentiation
50%
+0 −0
A formal-logic formula for decimal to binary conversion

3 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by r~~‭

bases conversion
50%
+1 −1
Rules of checking differentiability for Rolle's theorem

0 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

calculus real-analysis limits differentiability rolle's-theorem
50%
+0 −0
Second mean value theorem proof (differentiation)

0 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

calculus real-analysis differentiation
33%
+0 −2
If k = 1, why $n(n-1) \dots \color{red}{(n-k+1)} = n$?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
28%
+0 −3
Why shouldn't the Bose-Einstein value be used to calculate birthday probabilities?

0 answers  ·  posted 3y ago by DNB‭

probability
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