User David

4 votes

1 answer

2k views

Lagrange polynomial in 3-D. Variable of interest is a vector.

lagrange-interpolation

asked Jan 15, 2017 at 21:55

3 votes

2 answers

575 views

Correlation between 2 random variables and $\cos(\theta)$ on vector space

asked Jul 21, 2020 at 19:43

3 votes

1 answer

222 views

Probability that amoeba population dies out completely - why can't the probability be 1?

probability expected-value

asked Sep 10, 2020 at 4:58

3 votes

3 answers

57 views

$\binom{n}{j} \cdot (n - j)$ when $j = n$

binomial-coefficients

asked Apr 2, 2021 at 16:54

2 votes

3 answers

215 views

How to seat $n$ people in $n$ seats if each person must take a seat next to an already sitting person?

combinatorics

asked Jul 26, 2020 at 18:50

2 votes

2 answers

51 views

Expectation of the minimum of two continuous random variables - using the joint pdf

probability expected-value

asked Apr 19, 2021 at 13:29

2 votes

2 answers

88 views

Rolling a dice a maximum of two times, what is the expected sum of values?

probability expected-value

asked May 1, 2021 at 4:12

2 votes

1 answer

78 views

$f_X(x) \neq \frac{2 \pi \sqrt{R^2 - x^2}}{4\pi R^2}$? $X$ belongs to points uniformly distributed on the surface of a sphere.

probability

asked Aug 12, 2020 at 16:10

2 votes

0 answers

55 views

How to derive a generic formula for $\sum_{k=0}^n k^p$ for any $p$? [duplicate]

sequences-and-series

asked Aug 19, 2020 at 15:59

2 votes

2 answers

51 views

What is the difference between $P(S = s, N = n )$ vs $P(S = s | N =n)$

probability conditional-probability

asked Jul 4, 2020 at 4:15

2 votes

2 answers

71 views

Maximizing the quantity $f = -20p\cdot q + 9p + 9q$

calculus optimization

asked Jul 19, 2020 at 18:42

2 votes

1 answer

97 views

Why is $\operatorname{Var}(X_{(1)}) = \operatorname{Var}(X_{(n)})$ for i.i.d $X_1, \ldots, X_n \sim U(0,1)$?

probability expected-value uniform-distribution variance order-statistics

asked May 6, 2020 at 2:16

2 votes

1 answer

101 views

Expected number of tosses of getting $n$ heads in a row

conditional-expectation expected-value

asked May 12, 2020 at 2:15

1 vote

3 answers

134 views

jointly discrete continuous & discrete probability - conditioning on a range

probability conditional-probability

asked Mar 30, 2020 at 18:27

1 vote

1 answer

32 views

Probability of choosing an edge twice in a tetrahedron

probability conditional-probability

asked Jun 5, 2020 at 2:49

1 vote

1 answer

214 views

Extension of median minimizing the sum of absolute deviations (the $L_1$ norm)

optimization normed-spaces lagrange-multiplier median

asked Jun 22, 2020 at 18:14

1 vote

1 answer

33 views

How does $r$ for univariate regression relate to the general definition of $R^2$?

regression least-squares correlation

asked Jun 27, 2020 at 22:14

1 vote

0 answers

101 views

Order of accuracy of least squares for computing gradients

numerical-methods least-squares standard-error truncation-error

asked May 3, 2018 at 20:38

1 vote

1 answer

182 views

Expected number of tosses to get 2 heads in a row - what is wrong with my approach?

probability

asked Mar 27, 2020 at 20:21

1 vote

1 answer

20 views

If event $A$ happens with probability $p$, then when is event $B$ guaranteed to not be mutually exclusive with $A$?

probability inclusion-exclusion

asked May 4, 2020 at 21:13

1 vote

1 answer

53 views

Maximum likelihood estimation steps

probability maximum-likelihood

asked Jul 19, 2020 at 1:08

1 vote

3 answers

152 views

Probability that $\max(X_1, \ldots, X_n) - \min(X_1, \ldots, X_n) \leq 0.5$

probability uniform-distribution order-statistics

asked Jul 22, 2020 at 0:38

1 vote

1 answer

21 views

What is the simplest way to compute $f_Z(z)$ when $Z = \min(X, Y), X \sim U(0, 5), Y \sim U(0, 10)$?

probability order-statistics

asked Apr 19, 2021 at 13:44

1 vote

2 answers

160 views

Strict (or lack therefore) concavity of square root function

convex-analysis jensen-inequality

asked May 5, 2021 at 0:53

1 vote

2 answers

64 views

How to factor $ 1 - 3x + x^2 + x^3$?

polynomials factoring

asked Sep 10, 2020 at 4:37

1 vote

1 answer

37 views

Probability of median of 3 values drawn from $U(0, 1)$ being less than $c$?

probability uniform-distribution

asked Aug 9, 2021 at 3:13

1 vote

2 answers

49 views

Ball painting probability

probability

asked Jul 30, 2020 at 4:34

1 vote

2 answers

18 views

What is meant by $\log_2 X \sim N(0,n) \implies \log X \sim N(0, n (\log 2)^2)$?

logarithms normal-distribution

asked Apr 17, 2021 at 22:06

0 votes

1 answer

36 views

Why is $\exp(n/2 * (\log 2)^2) \approx 1.27^n$

exponentiation approximation

asked Apr 18, 2021 at 1:00

0 votes

1 answer

66 views

Why is the marginal pdf of $x$ on the surface of a sphere uniformly distributed, intuitively speaking?

probability marginal-distribution

asked Apr 16, 2021 at 13:38

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58 Questions

Lagrange polynomial in 3-D. Variable of interest is a vector.

Correlation between 2 random variables and $\cos(\theta)$ on vector space

Probability that amoeba population dies out completely - why can't the probability be 1?

$\binom{n}{j} \cdot (n - j)$ when $j = n$

How to seat $n$ people in $n$ seats if each person must take a seat next to an already sitting person?

Expectation of the minimum of two continuous random variables - using the joint pdf

Rolling a dice a maximum of two times, what is the expected sum of values?

$f_X(x) \neq \frac{2 \pi \sqrt{R^2 - x^2}}{4\pi R^2}$? $X$ belongs to points uniformly distributed on the surface of a sphere.

How to derive a generic formula for $\sum_{k=0}^n k^p$ for any $p$? [duplicate]

What is the difference between $P(S = s, N = n )$ vs $P(S = s | N =n)$

Maximizing the quantity $f = -20p\cdot q + 9p + 9q$

Why is $\operatorname{Var}(X_{(1)}) = \operatorname{Var}(X_{(n)})$ for i.i.d $X_1, \ldots, X_n \sim U(0,1)$?

Expected number of tosses of getting $n$ heads in a row

jointly discrete continuous & discrete probability - conditioning on a range

Probability of choosing an edge twice in a tetrahedron

Extension of median minimizing the sum of absolute deviations (the $L_1$ norm)

How does $r$ for univariate regression relate to the general definition of $R^2$?

Order of accuracy of least squares for computing gradients

Expected number of tosses to get 2 heads in a row - what is wrong with my approach?

If event $A$ happens with probability $p$, then when is event $B$ guaranteed to not be mutually exclusive with $A$?

Maximum likelihood estimation steps

Probability that $\max(X_1, \ldots, X_n) - \min(X_1, \ldots, X_n) \leq 0.5$

What is the simplest way to compute $f_Z(z)$ when $Z = \min(X, Y), X \sim U(0, 5), Y \sim U(0, 10)$?

Strict (or lack therefore) concavity of square root function

How to factor $ 1 - 3x + x^2 + x^3$?

Probability of median of 3 values drawn from $U(0, 1)$ being less than $c$?

Ball painting probability

What is meant by $\log_2 X \sim N(0,n) \implies \log X \sim N(0, n (\log 2)^2)$?

Why is $\exp(n/2 * (\log 2)^2) \approx 1.27^n$

Why is the marginal pdf of $x$ on the surface of a sphere uniformly distributed, intuitively speaking?