122,463 reputation
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bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 4 months
seen 5 hours 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


Jul
6
comment Joint probability of two conditional probabilities
What does $A|B \cap B|A$ mean? Note that $A|B$ and $B|A$ are not events.
Jul
6
answered Sequence of bounded linear operators implicating Cauchy sequence in $\mathbb K$
Jul
6
revised Constructing regular integer matrices with distinct integer eigenvalues
added 933 characters in body
Jul
6
answered Constructing regular integer matrices with distinct integer eigenvalues
Jul
6
answered Spectral norm proof (without the knowledge of eigenvector)
Jul
4
comment Initial value of Newton Raphson Method
... hopefully one where this condition holds all the way to a root. Then Newton-Raphson will converge monotonically to that root.
Jul
4
answered To minimize $x^TAx$ where $A$ is not necessarily positive semi-definite with constrains?
Jul
4
answered Initial value of Newton Raphson Method
Jul
4
answered Infimum of Gamma distribution
Jul
3
answered Which way will produce the following integral?
Jul
3
answered Representation theory in physics
Jul
3
answered Integrating $\iint_R \sin(9x^2+4y^2)\ dA$
Jul
3
comment Expectation of stopping time $\inf\left\{t: W_t>t\right\}$
A fundamental property of the Wiener process is that it is a Gaussian process. Depending on your approach, this is either part of the definition or one of the first theorems.
Jul
3
comment How far will my car roll given a function representing the slope of the landscape I'm driving on?
There had better be acceleration, or I'll never get my car out of the driveway. The velocity is not expected to be constant. You need a term $m \dfrac{d^2 x}{dt^2}$.
Jul
3
answered Taylor series of the function $f(x) = (1+x) ^{\frac{1}{x}}$
Jul
3
comment How far will my car roll given a function representing the slope of the landscape I'm driving on?
What kind of friction? The dependence of frictional force on velocity can be a complicated thing.
Jul
3
comment calculating moments of random variables
Of course this is not "in general" because you're given that it's a Gaussian process, so everything is determined by the means and covariances.
Jul
3
comment Expectation of stopping time $\inf\left\{t: W_t>t\right\}$
The covariance matrix of $X_1, \ldots, X_n$. Jointly normal random variables are independent if they are uncorrelated.
Jul
1
answered Probabilities of members leaving a team
Jul
1
comment Expectation of stopping time $\inf\left\{t: W_t>t\right\}$
If $Z_1, \ldots, Z_n$ are independent standard normal, $P(\text{ at least one}\ Z_k > 0) = 1 - 1/2^n$. For $X_1, \ldots, X_n$ that are jointly normal with mean 0 but not independent, $P(\text{ at least one}\ X_k > t_k^{1/2})$ is a continuous function of $t_1, \ldots, t_n$ and the covariance matrix.