A robot arm solders a component on a motherboard. The arm has(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Probability with expectation and variance

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