All Questions
Tagged with sum independence
7
questions
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154
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The third central moment of a sum of two independent random variables
Is it true that in probability theory the third central moment of a sum of two independent random variables is equal to the sum of the third central moments of the two separate variables?
- 11
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Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?
If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
- 23
2
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For k independent variables, if each one is independent of $Y_1$,...,$Y_p$, how to formally prove their sum is also independent of each $Y_p$?
SUppose I have $X_1,...,X_k$ independent of each other. I also have $Y_1,...,Y_p$ is independent of each other. If each one in $X_1$,...,$X_k$ is independent of each one in $Y_1$,...,$Y_p$, how to ...
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Independence of random variables and sums of random variables
I am seeking to find the joint distribution of X and Y. I have the marginal distributions of X and X+Y and they are independent.
We have that $f(X=x,Y=y)=f(X=x,X+Y=x+y)$ which is equal to $f(X=x)f(X+...
- 459
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2
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Is the error term a sum of r.v.?
`If in a econometric model I have:
$y = \beta x + u$
where u is the error term, we have:
$u = y - \beta x$
Supposing that $\beta=1$, $y\sim N(0,1)$, $x \sim N(0,1)$ and $x$, $y$ are independent.
...
- 55
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Correlation between Weighted Sum of Random Variables and Individual Random Variables
Given the following set of random variables and constants,
$\newcommand{\inreala}[2]{\in \mathbb{R}^{#1 \times #2}}
\newcommand{\var}{\mathrm{Var}}
\newcommand{\cov}{\mathrm{Cov}}
\newcommand{\corr}{\...
- 134
6
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multi stage binomial "process"
I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution
$$
X_1 \sim \text B(K,p)
$$
, p is the ...
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