Intereting Posts

Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
How would you explain why “e” is important? (And when it applies?)
Find the coordinates of a point on a circle
Is every nonzero integer the discriminant of some algebraic number field?
The logarithm is non-linear! Or isn't it?
What will be the value of the following determinant without expanding it?
Computing the coefficient in a large polynomial
Less than or equal sign
Find sum of the Trignomertric series
Aggregate arrivals from a renewal process
Kernel of the homomorphism $\mathbb C → \mathbb C$ deﬁned by $x→t,y→ t^{2},z→ t^{3}$.
Who gave you the epsilon?
How to find the limit without L'Hospital?
Two questions about Euler's number $e$
How to prove this equality .

I know that $E[E(X\mid Y,Z)\mid Y]=E(X\mid Y)$.

What if $E[E(X\mid Y)\mid Y,Z]=?$ It has any meaning?

- Conditional expectation of independent variables
- Understanding the measurability of conditional expectations
- Computing expectation of: $\small E\left $
- Fubini's theorem for conditional expectations
- Is it true that $\mathbb{E}+|\mathbb{E}\rvert\geq\mathbb{E}\rvert]+\mathbb{E}\rvert]$?
- Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$

- Help with a Probability Proof
- Bivariate Normal Conditional Variance
- marginal probability mass functions
- Flip a fair coin until three consecutive heads or tails appear
- Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
- Probability that an integer number having Poisson distribution is even
- Please correct my answer (Probability)
- Why is it that shuffling a deck so that all permutations are equally likely requires swapping only later elements?
- If $X$ and $Y$ are independent then $f(X)$ and $g(Y)$ are also independent.
- Probability of N unrelated events, each with different probabilities, what is the chance X number of outcomes occur

$E(X|Y)$ is $Y$-measurable and thus $Y,Z$-measureable so can still be pulled out of the conditional expectation. So $E(E(X|Y)|Y,Z) = E(X|Y)$

It’s like asking about $E(f(Y)|Y,Z)$. The $Z$ might seem to complicate things, but the fact that we’re conditioning on $Y$ means we can treat the $f(Y)$ as constant and pull it out of the expectation, giving $f(Y)E(1|Y,Z) =f(Y).$

- Solving an ordinary differential equation with initial conditions
- Square root of compact operator
- Help me to prove that group is cyclic
- Problems with Inequalities
- Prime factor of $A=14^7+14^2+1$
- Solving a difference equation with several parameters
- Why does $\mathrm{ord}_p(n!)=\sum_{i=1}^k a_i(1+p+\cdots+p^{i-1})$?.
- How to prove that the implicit function theorem implies the inverse function theorem?
- If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
- Distance function on complete Riemannian manifold.
- $\text{Sup}\{x\geq0:\sum\limits_{n=1}^\infty x^{\sqrt n}<\infty \}$
- How many sequences of $n$ tosses of a coin that do not contain two consecutive heads have tails as the first toss?
- If every convergent subsequence converges to $a$, then so does the original bounded sequence (Abbott p 58 q2.5.4 and q2.5.3b)
- The Affine Property of Connections on Vector Bundles
- Are “if” and “iff” interchangeable in definitions?