All Questions
Tagged with sum normal-distribution
26
questions
0
votes
0
answers
92
views
How to add noise into a standard distribution without increasing its variance?
Suppose I have a standard distribution dataset X with a mean 0 and std 1.
Now I want to create slight variations of this data by injecting some noise.
I could make ...
- 181
-1
votes
1
answer
200
views
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
1
vote
1
answer
266
views
2 approaches for Monte-Carlo : weighted sum of $\chi^2$ distribution and Moschopoulos distribution with Gamma distribution
If I take as definition of $a_{lm}$ following a normal distribution with mean equal to zero and $C_\ell=\langle a_{lm}^2 \rangle=\text{Var}(a_{lm})$, and if I have a sum of $\chi^2$, can I write the 2 ...
user226073
1
vote
1
answer
236
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Expectation of Maximum and Minimum of Partial Sums of Normal Random Variables
Peggy Strait, 1974, Pacific Journal of Mathematics
ON THE MAXIMUM AND MINIMUM OF PARTIAL SUMS OF RANDOM VARIABLES
Gives a nice result (4.3) and (4.4) in terms of "standard normal random variables&...
- 241
1
vote
1
answer
45
views
Sum of estimated costs for uncertain events
I have a number of possible events $e$ with a probability $p_e$ of the event occuring and a cost estimate should the event occur (if it doesn't occur the cost is 0). The probability for each event is ...
- 13
3
votes
1
answer
140
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What is the expectation of $\left\langle (n \bar{y})^4 \right\rangle$, if $y_i \sim \mathcal{N}(\mu,\sigma^2)$?
Let $y_i \sim \mathcal{N}(\mu,\sigma^2), \; i = 1,\ldots,n$ and $\bar{y} = \frac{1}{n} \sum_{i=1}^n y_i$, such that $n \bar{y} = y_1 + \ldots + y_n$.
Then, we want to know what the expectation of $(n \...
- 114
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answers
299
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Sum of IID normal variables with index following Poisson distribution
$X_1, X_2,\ldots$ are a sequence of independent normal random variables with mean 1 and variance 1.
Calculate the variance of $X_1+X_2+X_3+\ldots+X_{N+1}$ where $N$ follows Poisson distribution with ...
- 1
1
vote
1
answer
119
views
How to evaluate Probability of Y?
Hi all,
It's my first undergraduate statistics module as a business major and I've encountered some difficulties in computing the response to the question.
I have several queries below:
Would Y have ...
1
vote
1
answer
953
views
Distribution sum of correlated normal variables squared
I'm trying to deduce which distribution my data follows and how to estimate the parameters. I have four random variables $X_i \sim N(\mu_i,\sigma_i^2)$ where the means and variances are all different. ...
- 113
5
votes
1
answer
578
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How do I find the conditional distribution of a normal r. v. z, given that I know the sum of z and another normal r. v. x is greater than some value?
Suppose I have two independent normal random variables, $X$ and $Z$ with $\mu_x$, $\sigma^2_x$ and $\mu_z$, $\sigma^2_z$. Suppose I also know that $x+z\geq y$. How do I find the conditional ...
- 53
2
votes
2
answers
1k
views
Why is the sum of all the elements in a Gaussian-distributed list with zero mean not zero?
If I generate a list of elements from a Gaussian distribution with zero mean using Python
List = np.random.normal(0, 1, 500)
my intuition (why is obviously wrong) ...
- 145
4
votes
2
answers
1k
views
Does the sum of discrete uniforms converge to a discrete Gaussian?
Is there some analogous of the Central limit theorem for discrete uniforms and discrete normal distributions?
To be more specific, let's say we have identical and independent random random variables $...
2
votes
2
answers
147
views
Inferring random variables from their sum
Suppose I have a large set of receipts that list the items I bought, but only list the total cost. One day I might have bought Milk, Butter, and Eggs. A different day I might have bought Bread, Milk,...
- 473
5
votes
2
answers
621
views
Deconvolution of the sum of three gaussian distributions
Consider the sum of three normal random variables:
$
R_{i,j}=A_{i}+B_{j}+C_{i,j}\,
$
where
$
A_{i}∼N(μ_{A},σ_{A})
$
,
$
B_{j}∼N(μ_{B},σ_{B})
$
and
$
C_{i,j}∼N(μ_{C},σ_{C})
$
. Assuming $A$, $B$ ...
- 53
0
votes
1
answer
117
views
Summation of two Gaussian distributed data with different coefficient of mean and variance
I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them?
...
