## GR9768 Q 47

Forum for the GRE subject test in mathematics.
mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### GR9768 Q 47

Let x and y b uniformly distributed, independent random variables on [0,1]. The probability that the distance between x and y is <1/2 is

A) 1/4
B) 1/3
C) 1/2
D) 2/3
E) 3/4

EugeneKudashev
Posts: 27
Joined: Tue Apr 06, 2010 8:22 am

### Re: GR9768 Q 47

that is easy, man, just draw a pic.
you want the following to be satisfied: |x-y|<0.5
that becomes
x-y < 0.5 and x-y > -0.5
which is equivalent to
y > x-0.5 and y < x + 0.5
now draw a unit square [0,1]x[0,1], abscissa represents variable X, and ordinate corresponds to variable Y. draw these two lines above, I mean, plot the inequalities. you'll get the region between two parallel lines, and its area is just what you need - that is the probability of |x-y|<0.5. it's easy to figure out the area, I leave it up to you

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