# Probability with expectation and variance

1. Oct 23, 2012

### chupi1289

A robot arm solders a component on a motherboard. The arm has
small tiny errors when locating the correct place on the board. This
exercise tries to determine the magnitude of the error so that we know
the physical limitations for the size of the component connections. Let
us say that the right place to be soldered is the origin (0,0), and the
actual location the arm goes to is (X,Y ). We assume that the errors
X and Y are independent and have the normal distribution with mean
0 and a certain standard deviation sigma.
(a) What is the density function of the distance
D = SQRT ( X^2 + Y^2)

(b) Calculate its expected value and variance:
E(D) and Var(D)

(c) Calculate
E[|X^2 - Y^2|]

Ok so I changed to polar and have my joint pdf as follows:

(r/sigma^2) * e^(-r^2/2sigma^2) *1/2pi

Don't know how to calculate expectation and variance. I think I'm doing it wrong

2. Oct 23, 2012