J**********g
发帖数: 213 | 1 I happened to see a website that collects interview problems from all
companies. I think it's pretty good, and actually I find some interview
problems that do not appear here. Here are some interview problems that I
haven't seen here. So I put them here and hope to be useful for future
interviewees. Questions are for Morgan Stanley (questions in #4 are for
techical ones).
1. In a set of cereals, there are 4 kinds of coupons.
A child wants to collect all the 4 kinds of coupons.
How many boxes in |
J**********g
发帖数: 213 | 2 BTW, anyone knows the answers to the first two? I just wanna ensure the
correctness of the answers.
Also I have an interview with MS tomorrow afternoon...please wish me good
luck....thank you dude. |
k*******d
发帖数: 1340 | 3 1. Google "coupon collector problem"
2. simple optimization: 0.3x^2 + 0.2 (1-x)^2 + 2*sqrt(0.3)sqrt(0.2）*0.5*(1-x)*x
minimize over x, no more constraints |
m*******r
发帖数: 98 | 4 odd
I
【在 J**********g 的大作中提到】
: I happened to see a website that collects interview problems from all
: companies. I think it's pretty good, and actually I find some interview
: problems that do not appear here. Here are some interview problems that I
: haven't seen here. So I put them here and hope to be useful for future
: interviewees. Questions are for Morgan Stanley (questions in #4 are for
: techical ones).
: 1. In a set of cereals, there are 4 kinds of coupons.
: A child wants to collect all the 4 kinds of coupons.
: How many boxes in
|
k*******d
发帖数: 1340 | 5 3. what is the relation between wiener process and martingale
Wienner Proc is a Martingale.
4. (Position:Model Review at Morgan Stanley) The technical interview
consisted of the following:
for a<0
before b?
|a|/(|a|+b)
What is the expectation of the first hitting time of a or b?
\infty
What is B_t^2 (super or submartingale)
Submartingale
For X and Y two independent exponential variables with parameters a and b,
compute P(X>Y).
Giv |
J**********g
发帖数: 213 | 6 why? :-)
【在 m*******r 的大作中提到】
: odd
:
: I
|
k*******d
发帖数: 1340 | 7 sorry....
You are right...
I will revise my post...
【在 J**********g 的大作中提到】
: why? :-)
|
k*******d
发帖数: 1340 | 8 Most of these questions have been seen a lot of times in this BBS...
【在 J**********g 的大作中提到】
: why? :-)
|
J**********g
发帖数: 213 | 9 Thank you first for answering questions for me. I am PhD in math, but not in
this kind of stuff. I am try to learn things by myself, but I need to some
assurance, and I really don't wanna make any mistake tomorrow. Thank you
again.
PS. I deleted my post for #2.
【在 k*******d 的大作中提到】
: Most of these questions have been seen a lot of times in this BBS...
|
k*******d
发帖数: 1340 | 10 For X and Y two independent exponential variables with parameters a and b,
compute P(X>Y).
这题有人会简便方法么？
Thanks. |
|
|
s*******u
发帖数: 35 | 11 P(X>Y)=\sum_{i=0}^{\infty}\sum_{j>i}P(X=j)P(Y=i)
It can be simplified because of exponential distribution.
b,
【在 k*******d 的大作中提到】
: For X and Y two independent exponential variables with parameters a and b,
: compute P(X>Y).
: 这题有人会简便方法么？
: Thanks.
|
L******2
发帖数: 274 | 12 the joint pdf of X and Y is a*e^(-ax)*b*e^(-by). integrate this over the
region x-y>0 you will get b/(a+b.)
【在 k*******d 的大作中提到】
: For X and Y two independent exponential variables with parameters a and b,
: compute P(X>Y).
: 这题有人会简便方法么？
: Thanks.
|
t*******y
发帖数: 637 | 13 为什么我积分出来时infinity?
【在 L******2 的大作中提到】
: the joint pdf of X and Y is a*e^(-ax)*b*e^(-by). integrate this over the
: region x-y>0 you will get b/(a+b.)
|
f********y
发帖数: 278 | 14 P(X>Y)=\int_0^{\infty} f(x)*P(x
=\int_0^{\infty} f(x)*P(x
=...
【在 k*******d 的大作中提到】
: For X and Y two independent exponential variables with parameters a and b,
: compute P(X>Y).
: 这题有人会简便方法么？
: Thanks.
|
i*******g
发帖数: 276 | |
c****o
发帖数: 1280 | 16
I think it is b/(b-a), not -a in the numerator.....any thought?(Think about
a=0.
I do not think so....in this case, w^2(t)-t is the martingale, use OST, we
know
E(\tau)=E(w^2(\tau))=a^2*p(w(\tau=a)+b^2*p(\tau=b))
【在 k*******d 的大作中提到】
: 3. what is the relation between wiener process and martingale
: Wienner Proc is a Martingale.
: 4. (Position:Model Review at Morgan Stanley) The technical interview
: consisted of the following:
: for a<0: before b?
: |a|/(|a|+b)
: What is the expectation of the first hitting time of a or b?
: \infty
: What is B_t^2 (super or submartingale)
|
c****o
发帖数: 1280 | 17
I think it is b/(b-a), not -a in the numerator.....any thought?(Think about
a=0.
I do not think so....in this case, w^2(t)-t is the martingale, use OST, we
know
E(\tau)=E(w^2(\tau))=a^2*p(w(\tau=a)+b^2*p(\tau=b))
【在 k*******d 的大作中提到】
: 3. what is the relation between wiener process and martingale
: Wienner Proc is a Martingale.
: 4. (Position:Model Review at Morgan Stanley) The technical interview
: consisted of the following:
: for a<0: before b?
: |a|/(|a|+b)
: What is the expectation of the first hitting time of a or b?
: \infty
: What is B_t^2 (super or submartingale)
|
k*******d
发帖数: 1340 | 18 你是对的。。我太粗心了。。。
sorry...
about
we
【在 c****o 的大作中提到】
:
: I think it is b/(b-a), not -a in the numerator.....any thought?(Think about
: a=0.
: I do not think so....in this case, w^2(t)-t is the martingale, use OST, we
: know
: E(\tau)=E(w^2(\tau))=a^2*p(w(\tau=a)+b^2*p(\tau=b))
|
J**********g
发帖数: 213 | 19 I just realized that I have the book....anyway, I don't know if I need it for the second round now...
【在 i*******g 的大作中提到】
: xinfeng的书上不都有嘛？
|
x******a
发帖数: 6336 | 20 2. what does it mean by a minimum risk?
minimize the variance of a linear combination of the two stock?
I
【在 J**********g 的大作中提到】
: I happened to see a website that collects interview problems from all
: companies. I think it's pretty good, and actually I find some interview
: problems that do not appear here. Here are some interview problems that I
: haven't seen here. So I put them here and hope to be useful for future
: interviewees. Questions are for Morgan Stanley (questions in #4 are for
: techical ones).
: 1. In a set of cereals, there are 4 kinds of coupons.
: A child wants to collect all the 4 kinds of coupons.
: How many boxes in
|
J**********g
发帖数: 213 | 21 minimum risk=minimum variance, so just minimize the variance of combination
of stocks...
I will post all questions and answers online after I finish it. hope to get it. |
