# Homework Help: Probability and Statistics

1. Feb 19, 2006

### Bunting

Hiya, this is second year UG Coursework (worth very little) so I dont want any "answers" to the questions (else its plagarism ;)) but hints in the right direction if you will :)

Question 1
A random walker takes one step to the right with probability p times that with which she takes p successive steps to the left. Show that her typical distance from the origin grows like sqrt(p).

Question 2
Variables x1 and x2 are drawn independently from two Gaussian distributions with means µ1 and µ2, and standard deviations sigma1 and sigma2 respectively. What are the mean values and standard deviations of x1 + x2 and x1x2?

I have found the first answer (x1+x2) to this using moment generating functions, but I cant find a way to apply this method to x1x2. edit: I think i have foudn the answer to part 2 as well, in a manner of speaking. It seems some reasearch has been recently written on the subject, which is rather annoying. It didn't help much, but ive got some form of an answer.

Question 3
An archer’s aim has a Gaussian distribution about the centre of a circular target. If the standard distribution is such that he hits the target 50% of the time, by how much must he reduce the standard deviation to hit 90% of the time?

With this can i simply approximate a normal distribution to a binomial distribution ?

Thanks a bunch for any suggestions/pointers in the right direction :)

Last edited: Feb 20, 2006