Question

For linearly independent vectors {u, v}, {$ au+bv, cu+dv$} is linearly independent iff $\begin{pmatrix}a & b\\\ c & d\end{pmatrix}$ is invertible.

score 806 · Answer 1 · 2020-01-21 09:21:41

806

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For linearly independent vectors {u, v}, {$ au+bv, cu+dv$} is linearly independent iff $\begin{pmatrix}a & b\\\ c & d\end{pmatrix}$ is invertible.

Published on 21 Jan 2020 - 9:21

score 311 · Answer 2 · 2026-03-25 07:46:06

311

Views

Moments of products of independent random variables: $E[X^mY^n]$ Part II

Published on 25 Mar 2026 - 7:46

score 180 · Answer 3 · 2020-01-22 20:33:23

180

Views

What is $P(X < Y)$ when joint pdf is $f(x,y) = 2ye^{-xy-2y}\mathbb{1}_{[0, \infty) \times [0, \infty)}(x,y)$?

Published on 22 Jan 2020 - 20:33

score 48 · Answer 4 · 2020-01-23 01:52:32

48

Views

How to prove that pairs of probability are independent?

Published on 23 Jan 2020 - 1:52

score 252 · Answer 5 · 2020-01-23 20:48:00

252

Views

Is it feasible to prove this property of conditional expectation without too many lemmas?

Published on 23 Jan 2020 - 20:48

score 41 · Answer 6 · 2020-01-24 20:05:34

41

Views

Checking for linear independence of rows vs columns?

Published on 24 Jan 2020 - 20:05

score 193 · Answer 7 · 2020-01-25 20:15:17

193

Views

Infinite sequence of RV's on finite sample space

Published on 25 Jan 2020 - 20:15

score 127 · Answer 8 · 2020-01-27 20:14:08

127

Views

If $X_2$ is independent of $\mathcal F$, can we show that $f(X_1,X_2)$ is conditionally independent of $\mathcal F$ given $X_1$?

Published on 27 Jan 2020 - 20:14

score 167 · Answer 9 · 2020-01-29 01:05:37

167

Views

Bounds when integrating a certain joint probability density function

Published on 29 Jan 2020 - 1:05

score 33 · Answer 10 · 2020-01-29 18:11:24

33

Views

How to find the probability of an event "B" when given the probability of event A and the probability of the union of A and B?

Published on 29 Jan 2020 - 18:11

score 32 · Answer 11 · 2020-01-29 23:49:08

32

Views

Brownian motion independent from a random variable

Published on 29 Jan 2020 - 23:49

score 63 · Answer 12 · 2026-03-27 16:39:55

63

Views

Conditional Independence Relations for $X_1\leftarrow X\rightarrow X_2$

Published on 27 Mar 2026 - 16:39

score 118 · Answer 13 · 2020-01-31 01:38:35

118

Views

Dependency for coin toss

Published on 31 Jan 2020 - 1:38

score 48 · Answer 14 · 2020-01-31 10:17:46

48

Views

Why are the two events independent of each other in this case?

Published on 31 Jan 2020 - 10:17

score 178 · Answer 15 · 2026-03-28 15:12:48

178

Views

How to get conditional probability from joint conditional probability?

Published on 28 Mar 2026 - 15:12

List Question

For linearly independent vectors {u, v}, {$ au+bv, cu+dv$} is linearly independent iff $\begin{pmatrix}a & b\\\ c & d\end{pmatrix}$ is invertible.

Moments of products of independent random variables: $E[X^mY^n]$ Part II

What is $P(X < Y)$ when joint pdf is $f(x,y) = 2ye^{-xy-2y}\mathbb{1}_{[0, \infty) \times [0, \infty)}(x,y)$?

How to prove that pairs of probability are independent?

Is it feasible to prove this property of conditional expectation without too many lemmas?

Checking for linear independence of rows vs columns?

Infinite sequence of RV's on finite sample space

If $X_2$ is independent of $\mathcal F$, can we show that $f(X_1,X_2)$ is conditionally independent of $\mathcal F$ given $X_1$?

Bounds when integrating a certain joint probability density function

How to find the probability of an event "B" when given the probability of event A and the probability of the union of A and B?

Brownian motion independent from a random variable

Conditional Independence Relations for $X_1\leftarrow X\rightarrow X_2$

Dependency for coin toss

Why are the two events independent of each other in this case?

How to get conditional probability from joint conditional probability?

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