# Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

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### Significance and Poisson processes

Must I include the Poisson error on a new observation when considering whether it is consistent with a distribution? For example, the number of rain drops that fall into a cup per minute are recorded....
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### Conditional expectation of independent normals

As it was proved in the answer here, for $Z_1, Z_2$, two independent and identically distributed random variables. Then we have: $$\mathbb E[Z_1\mid Z_1+Z_2] =\frac{Z_1+Z_2}{2}.$$ However, suppose ...
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### Hard time factoring Normal Distribution based on transformation problem.

My professor gave problems out to practice for our final on Wednesday. This problem is based on the transformation of two random variables. It a 5 part problem, so I will list the necessary portions ...
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### Bivariate normal distributed vector $X (X,Y)$. Show distribution of $(X-Y, X+Y)$.

I have a a bivariate normally distributed random vector $X = (X,Y)$ and with Expected Value $(X)= (\mu(x),\mu(y))$, and Covariance Matrix $2\times 2$. (not independent) Now I want to show which ...
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### Why is $\dfrac{b(3x)}{b(x\bigoplus2x)}$ almost normally distributed?
I'm sorry if my question is a bit vague; I don't know a whole lot about distributions. Let $b(x)$ be the number of ones in the binary representation of $x$. I use $\bigoplus$ as bitwise XOR operator. ...
Theorem. If $X$ and $Y$ are two independent normal random variables with means $a,b$ and variances $c,d$ respectly, the sum $X+Y$ is a normal random variable with parameters $a+b$ and $c+d$. My ...