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Oct
20
answered Equivalent definition of random variables
Oct
17
answered Sub-Martingale and Martingale
Oct
4
answered Doubt about conditional probability
Oct
4
answered For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$.
Oct
3
answered Stuck with a problem regarding conditional expectation
Sep
26
answered Definition of multivariate random variable
Sep
26
answered Prove that if expectations agree on a Pi-System, then they agree on the Sigma-Algebra generated by the Pi-System.
Sep
19
answered E[X|Y]=E[X] When X and Y are Independent — Proof from Book Question
Sep
19
answered Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
Sep
18
answered Question about the Central Limit Theorem
Sep
18
answered Expectation of a Random Variable multiplied by a Conditonal Expectation.
Sep
12
answered Algebra - Sums and Means of two sets
Sep
12
answered Let $f,g$ be $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions. I want to show piecewise function $h$ of $f$ and $g$ is also measurable.
Sep
12
answered Let $X$ be a non-empty set, $A \subseteq X$. Decide the set $\mathcal M(\mathcal{E})$ of $\mathcal{E}$-$\mathcal B(\mathbb R)$-measureable functions.
Sep
12
answered Let $(X,\epsilon)$ be a measurable space. Show $\mu: \epsilon \rightarrow [0, \infty]$ is a measure given three conditions.
Sep
9
answered Show limits of function $f(x) := \lambda(B \cap (-x,x])$ and there exist a Borel-set $A$ such that $A \subseteq B$ and $\lambda(A)=a$.
Sep
8
answered Given a CDF, find P(-.5<X<.5)
Sep
5
answered Computing absolute distribution from conditioned probability
Sep
5
answered Survival function in terms of the hazards
Sep
4
answered $X$ and $Y$ are independent and follow $U(0,1)$. Show $P(f(X) > Y) = \int_0^1 f(x) dx$