All Questions
8 questions
2
votes
1
answer
136
views
Concatenation of Distributions
I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
- 123
4
votes
5
answers
360
views
Expressions for moments of sample cumulants?
I sample $n$ points from standard normal and need the mean and variance of 3rd and 4th sample cumulants.
@JimB suggested that variance of 4th sample cumulant is given by the expression below. This ...
- 6,697
0
votes
3
answers
350
views
How can I calculate the expected value of the sum of "n" i.i.d. variables with any distribution?
Particulary, I would like to find the expected value of the sum of $n$ variables distributed like ParetoDistribution[1,1.14]. For example, this works for the sum of two vars with Gamma distribution:
<...
3
votes
2
answers
230
views
How do I check and justifiy a symbolic result returned by Mathematica?
Similar things have been asked previously (see https://academia.stackexchange.com/q/71536/4132 for instance), but I want to address the specific case in which a complex symbolic/analytical result has ...
- 1,121
3
votes
1
answer
249
views
How to get a more compact form of this probability calculation?
Inspired by the probability calculation here, I am trying to solve a little general one:
$$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} S_i)$...
- 840
7
votes
1
answer
493
views
How to solve this probability symbolically or numerically?
I am trying to calculate the following probability
$$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$
where,
$$A_i \sim \exp(\lambda), \quad S_i \sim \exp(...
- 840
2
votes
1
answer
614
views
Compute symbolic Expectation of a summation
I am required to computed following Expectations :
$E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = \frac{(N\bar{x}...
6
votes
2
answers
245
views
MarginalDistribution with Symbolic range in ProbabilityDistribution
Given the following joint density:
for 10 < x < 20, x/2 < y < x.
To find the marginal density for X we do:
...
- 33.3k