To probability lovers, I just want to share (and discuss) few simple problems I solved in Chapter 4 of Casella, G. and Berger, R.L. (2002). Statistical Inference . A random point (X,Y) is distributed uniformly on the square with vertices (1, 1),(1,-1),(-1,1), and (-1,-1). That is, the joint pdf is f(x,y)=\frac{1}{4} on the square. Determine the probabilities of the following events. X^2 + Y^2 < 1 2X-Y>0 |X+Y| Solutions: X^2 + Y^2 < 1 We need to consider the boundary of this inequality first in the unit square, so below is the plot of X^2 + Y^2 = 1$,
. . . a love story between theory and practice . . .