138,968 reputation
590232
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 8 months
seen 1 min ago

I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


4m
answered Conditional expectation of second moment given sum of iid variables.
25m
comment Does the function of a random variable have the same transition matrix as the variable itself?
Are you talking about a discrete state space or a continuous one? Your mention of "density" is confusing me.
29m
comment Bernoulli random variable uniformly distributed have same distribution as a subsequent binomial variable?
No, it is a hint.
30m
answered find a sequence converging to zero but not the elemet of lp space for every 1<_p<infinity
2h
comment Does the function of a random variable have the same transition matrix as the variable itself?
If the function $f$ is not one-to-one, $f(X_n)$ might not even be a Markov chain.
2h
comment Two questions on number 2013
Sum of an odd number of odd numbers is odd.
2h
answered Bernoulli random variable uniformly distributed have same distribution as a subsequent binomial variable?
19h
answered If $P(A_n) \ge \epsilon>0$ for large $n$, then $P(A_n i.o.) \ge \epsilon$
19h
answered Composition of two functions is not commutative
19h
comment Linear independence of Eigenvectors - repeated eigenvalue
Usually one might require $v_{n-1} \ne 0$ and $(A - \lambda_{n-1} I) v_n \ne 0$.
20h
answered Prove a certain matrix is positive semidefinte.
21h
answered The Burger's vortex in 2 Dimension - solving Differential equation
1d
comment Question on matrix exponential
Since they are simple eigenvalues, you don't need JCF: the matrix is diagonalizable.
1d
comment Probability that last child is a boy
We do need to know about it, because it affects the probabilities, just as the statement that he has more girls than boys does.
1d
comment On the constuction of a series of meromorphic functions that converges to a meromorphic function with prescribed poles and residues.
$z^3/k^3$ will work nicely. BTW, you might be interested to know that the sum has a closed form: $$\sum_{k=1}^\infty \dfrac{z^3}{k (z-k)} = z^2 (\gamma + \Psi(1-z))$$
1d
revised On the constuction of a series of meromorphic functions that converges to a meromorphic function with prescribed poles and residues.
deleted 2 characters in body
1d
comment On the constuction of a series of meromorphic functions that converges to a meromorphic function with prescribed poles and residues.
Thanks for catching that. I'll edit.
1d
comment Probability that last child is a boy
I guess we are to assume that his decisions on whether to have another child are independent of the genders of his existing children, but this assumption should be stated. It could be that he (and presumably his partner) kept having children until they had at least one boy and at least one girl, and then stopped. In that case, given that they have more girls than boys, the last one is definitely a boy.
1d
comment On the constuction of a series of meromorphic functions that converges to a meromorphic function with prescribed poles and residues.
... or e.g. you could just multiply $-k^2/(z-k)$ by a suitable factor. A certain exponential will work nicely.
1d
comment On the constuction of a series of meromorphic functions that converges to a meromorphic function with prescribed poles and residues.
The main problem with that series is that it diverges. But you say you know Mittag-Leffler's theorem...