All Questions
Tagged with sum density-function
5
questions
5
votes
1
answer
73
views
If $Z=X+Y$, and I know the probability distribution of $Z$ and $Y$, and $X\perp Y$ how to recover the probability distribution of X?
Suppose I know the distribution of $Z$ and $Y$: $Z\sim F_Z$ with density $f_Z$, $Y\sim F_Y$ with density $f_Y$. Suppose I also know that $Z=X+Y$, where $X$ and $Y$ are independent and the ...
- 2,966
-1
votes
1
answer
200
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Consistency when we want to find the distribution of sum of random variables following each one a distribution
I want to clarify a point that disturbs me among different cases.
I am interested in formulate correctly in a general case when we know the distribution of different random variables and we want to ...
user226073
0
votes
0
answers
396
views
Sum of a number of shifted exponentially distributed random variables
I know that the sum of $k$ independent exponentially distributed random variables each with density function:
$$\displaystyle \lambda\,{{\rm e}^{-\lambda\,x}}$$
has an Erlang distribution:
$$\...
- 305
1
vote
1
answer
634
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What is the probability density function (pdf) of the dot product of M complex normal random variables?
What would be the probability density function (pdf) of the complex random variable given below?
$$Z = \sum_{i=1}^{M}{x_{i}^{*}y_{i}}$$
where $x_i, y_i$ are independent r.v.'s with $\mathcal{CN}(0,c)...
3
votes
1
answer
115
views
Sum of function of normally distributed values
I have a given number, $v$, given by
$$v = \sum_{i=1}^N\left\{v_i \cdot \left[m \cdot \left(1 - b_i \cdot \mathbb{1}_{\geq w}(v_i)\right) - b_i \cdot \mathbb{1}_{< w}(v_i) \right] - a \cdot \mathbb{...
- 535