[944] Notes and typos

[Gautam Iyer]

On Mon, Feb 06, 2017 at 04:30:04PM -0500, Gautam Iyer via mscf-944 wrote:

> To reconfirm: I do not yet know the status about grading of HW4. I will
> let you know about this shortly. However, the homework is mainly
> practice with Itô's formula, so I recommend looking over it when
> studying for your exam.

Hi Guys,

In light of your midterm on 2/8, this homework 4 is optional. It will
not be graded, and solutions will not be posted. All the problems are
good exam practice, so I recommend trying them. Also, a few problems
will make their way to your next homework.

Problem 7.6 in the notes is from an interview this year. Steve tells me
that this is apparently a common question on interviews. I was hoping to
do this in class today, but ran out of time.

Here's how I recommend solving it:

    1. For X, use 7.5 to conclude that X(t) is normally distributed with
       mean 0 and variance t^2/2.

    2. For Y, show (in a manner similar to 7.5) that Y(t) is also
       normally distributed, with mean 0, and compute the variance.

Once you know this use the standard formulae to compute higher moments
of X and Y.

Problem 7.7 is on HW4 with a hint (and will certainly be on HW5).
Problem 7.8 was on HW3, and solutions to this are online.

GI

-- 
'Punctuality' -- The virtue of the bored.