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Apr
10
comment How do you handle this kind of probability?
The relevant modification of the setting of your question is well known: to draw the entries of the matrix according to a genuine probability measure (most notably, normal or Bernoulli).
Apr
10
comment How do you handle this kind of probability?
By the way, the relevant modification of the OP's question is not, as you suggest, to drop the finiteness of the measure but to draw the entries of the matrix according to a genuine probability measure (most notably, normal or Bernoulli).
Apr
10
comment How do you handle this kind of probability?
Which does not exclude $X=\mathbb R$ at all. Of course, if $\mathbb R$ is equipped with the Lebesgue measure, then the total mass is infinite. (Since you modified your answer to this effect after my comment was posted, you are aware that this was the problem with your original answer and I am not sure to understand your "Can you explain?" comment.)
Apr
10
answered relation between multivariate probability generating function and univariate ones
Apr
10
comment How do you handle this kind of probability?
"probability studies finite measure spaces (so $\mathbb{R}$ is excluded)" Quite untrue.
Apr
10
comment How do you handle this kind of probability?
Hence "Yeah, I know"?
Apr
10
comment multivariate probability generating function
Please do not modify drastically a question after some answers are posted. Instead, revert the changes and ask a new question.
Apr
10
comment How do you handle this kind of probability?
This is missing the crucial information of how you select a $3\times3$ matrix.
Apr
10
comment A die is loaded in such away an a probability
The data is insufficient to determine these quantities.
Apr
10
comment Distribution of the product of Gaussian column matrix and Signed Bernoulli matrix
Which paper? $ $
Apr
10
comment Showing series of a product converges to 0
Please replace $\to$ by $=$, twice.
Apr
10
comment Showing series of a product converges to 0
possible duplicate of showing a condition implies convergence to invariant distribution
Apr
10
revised Show that $\frac{1}{x^4 \sin^2 (x) +1} \in L^1([0, \infty))$
added 20 characters in body
Apr
9
answered Show that $\frac{1}{x^4 \sin^2 (x) +1} \in L^1([0, \infty))$
Apr
9
comment mathematical biology1
Please correct the misprints in (1) and/or (2).
Apr
9
answered multivariate probability generating function
Apr
9
comment multivariate probability generating function
The $X_i$s are independent?
Apr
9
comment Expected value of a sum starting at a value given through a random variable
Obviously there is no general expression in $(\mu,\sigma)$ only, the whole distribution is at play.
Apr
9
answered Event-level independence does not imply random-variable independence for non-binary random variables
Apr
9
comment Markov Process Feller Construction
You apply formulas that are valid in the discrete setting although, in this problem, the time is continuous. Have you ever seen the definition of the generator of a continuous time finite Markov process?