Intereting Posts

Maximum of $\frac{\sin z}{z}$ in the closed unit disc.
Solving the equation $ x^2-7y^2=-3 $ over integers
What is the meaning of normalization of varieties in complex geometry?
Two homologous but not homotopic loops on a closed surface of genus greater than one
Tensors = matrices + covariance/contravariance?
Lie algebra homomorphism preserves Jordan form
Proving there are infinitely many pairs of square-full consecutive integers
Techniques to prove a function is uniformly continuous
Finding prime factors by taking the square root
What is “Approximation Theory”?
Limits, find a limit that exist in absolute value but not outside the absolute value.
Is the derivative of an integral always continuous?
Definition of an ellipsoid based on its focal points
From $e^n$ to $e^x$
Integral $\int_0^1\frac{\arctan^2x}{\sqrt{1-x^2}}\mathrm dx$

Let $S \subset \mathbb{R}$ and let $Z$ be a standard normal random variable.

Let

\begin{align}

Z_1&=Z \cdot 1_{S},\\

Z_2&=Z \cdot 1_{S^c},

\end{align}

where $1_S$ is an indicator function and $S=[-a,a]$ for some $a>0$.

Can we find the distribution of ${Z_1}$ and $(Z_1,Z_2)$ and $Z_1 |Z_2$?

Thanks.

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