SERVING THE QUANTITATIVE FINANCE COMMUNITY

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by alexrem
November 4th, 2010, 6:38 pm
Forum: Careers Forum
Topic: Internships Question
Replies: 0
Views: 22842

Internships Question

<t>I am a junior at the University of Toronto looking for an internship for the summer of 2011. I know the Toronto financial jobs market is quite big, but I am interested in working in New York.Large investment banks and hedge funds have started accepting applications for internships, but the select...
by alexrem
October 13th, 2010, 2:14 am
Forum: Brainteaser Forum
Topic: generalizing the birthday problem
Replies: 3
Views: 26610

generalizing the birthday problem

For the first one use inclusion-exclusion principle; for the second just do 1 - P(nobody is born on specified date) - P(1 person bought that date)-...-P(k-1 people born on that date), each of the terms is easy to calculate.I am not sure if the answers simplify.
by alexrem
March 10th, 2010, 1:34 am
Forum: Student Forum
Topic: Covariance
Replies: 1
Views: 29510

Covariance

<t>By linearity of covariance you would have cov(x1, x2)=ac cov(r1, r1)+ bd cov (r2, r2) + (ad+bc)cov(r1, r2) = ac (v1)+ bd (v2) + (ad+bc)cov(r1, r2).You need to know the covariance between r1 and r2, knowing only their variances is not enough to do the question. By the way, you also need to know th...
by alexrem
March 1st, 2010, 2:33 am
Forum: Student Forum
Topic: Brownian Motion (Sojourn Time Problem)
Replies: 5
Views: 33317

Brownian Motion (Sojourn Time Problem)

<t>Hi, I have been trying this problem for some time now:Given $X(t)=\mu t+\sigma B(t)$ where $B(t)$ is standard Brownian motion, determine the expected amount of time spent in $(0, \delta)$.It is suggested to consider $Y=\int_{0}^{\infty} I{0<X(t)<\delta} dt$ and to find $E(Y)$.I am really not sure...
by alexrem
October 7th, 2009, 11:01 pm
Forum: Brainteaser Forum
Topic: random allocation
Replies: 97
Views: 41818

random allocation

<t>Maybe use recursion? Randomly generate x_n in [0, c], subtract it from 1, (if c is bigger than 1 you just take c=1), and then you need x_1+x_2+...+x_n-1 = (1-x_n) = a which is fixed. So now you scale down 1 to a so now you are generating randomly x_1+x_2+...+x_(n-1) = a with x_i in [0, c] which i...
by alexrem
August 13th, 2009, 4:41 pm
Forum: Brainteaser Forum
Topic: The isolated village
Replies: 24
Views: 41080

The isolated village

<t>QuoteOriginally posted by: twofishIs there a requirement that people die in an "orderly" way? If people die in a random way, does this throw off the induction?I think as long as the villagers know each others' dying times, they are ok, because then depeding on the amount of time passed, you can d...
by alexrem
August 13th, 2009, 4:07 pm
Forum: Brainteaser Forum
Topic: The isolated village
Replies: 24
Views: 41080

The isolated village

<t>I guess another way to explain that the white-dotted villagers die at time n if there are n white dots in total is the following:Consider one white-dotted person at time n. He sees n-1 dots and also that all those guys with the n-1 dots are alive. He assumes first he has a black dot. He considers...
by alexrem
May 14th, 2009, 12:46 am
Forum: Brainteaser Forum
Topic: another stick problem
Replies: 6
Views: 41168

another stick problem

<t>Call a break good if after the 2 breaks the longer piece has length greater than 3/5.Let the length of the smaller stick after the first break be x. Firstly, x<=1/2 (as it is the shorter piece).For each value of x in range 0 to 1/2 let f(x) be probability that when the piece 1-x is broken in 2 pa...
by alexrem
May 12th, 2009, 12:22 am
Forum: Brainteaser Forum
Topic: Prisoners and hats
Replies: 17
Views: 52848

Prisoners and hats

<t>I think this strategy might work:First the prisoners number the colors 1,2,....,M.Then prisoner n (just anybody will do) looks at all the other hats and does the following thing:for every prisoner i (i=1,2,...,n-1) he looks at his hat, and the adds the number of the color of this hat to the grand...
by alexrem
April 23rd, 2009, 10:01 pm
Forum: Brainteaser Forum
Topic: a gambler's ruin problem
Replies: 19
Views: 100693

a gambler's ruin problem

<t>QuoteOriginally posted by: cdmurray80Thats a random walk on a bridge right? e.g. a drunk man stands on position 7 of a bridge that has length 20, and takes one step left or right every turn. If he falls of the closer side A wins.I've seen this problem but I don't know an easy solution technique.....
by alexrem
April 4th, 2009, 9:25 pm
Forum: Careers Forum
Topic: Starting out early
Replies: 3
Views: 41105

Starting out early

Thanks for your advice, Yossarian22! @KackToodles: Yes, although in first year it is pretty basic. So far I have taken linear algebra and got a high 90, will finish calculus with probably also high 90, and will take C++ next yr. I have taken Java and got an A- there.
by alexrem
April 3rd, 2009, 5:52 pm
Forum: Careers Forum
Topic: Starting out early
Replies: 3
Views: 41105

Starting out early

<t>Hi, I am currently finishing my freshman yr at the University of Toronto studying a Specialist in Mathematical Applications in Economics and Finance. I have recently started doing some research about the quant career and the field of financial math in general, and I find it very interesting and a...
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