### Questions (31)

 19 Integral over null set is zero 7 Ratio test for sequences, the other direction 5 Understanding Direct Sum 5 $X,Y$ i.i.d., $X$ and $(X+Y)/\sqrt{2}$ have the same dist., then show that $X$ has a normal distribution 4 Any set with more elements than the dimension of vector space is linearly dependent

### Reputation (879)

 +10 Understanding Direct Sum +20 Integral over null set is zero +10 Rate of convergence of Riemann sum under Lipschitz +10 Strongly equivalent metrics are equivalent

 1 $E(X)$ given $f_{X,Y}$ 1 Covariance of conditional expectation is “orthogonal” 0 3 Events, Conditional Independence 0 $f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$ -1 Uniformly integrable for a random variable

### Tags (28)

 1 probability × 13 0 elementary-set-theory × 4 1 conditional-expectation × 2 0 examples-counterexamples × 3 1 covariance × 2 0 convergence-divergence × 3 0 real-analysis × 10 0 proof-writing × 3 0 probability-theory × 4 0 metric-spaces × 3

### Bookmarks (14)

 85 Easy math proofs or visual examples to make high school students enthusiastic about math [closed] 37 Rational + irrational = always irrational? 21 Proof of analogue of the Cauchy-Schwarz inequality for random variables 19 Up-to-date advice on the best way to take notes (maths) 11 From conditional probability to conditional expectation?