Saturday, January 16, 2010

Fox 229

2 comments:

  1. Answer is A.

    But I need integral calculus to solve it.

    By simmetry of circle, the expected value is two times the value on interval [0,pi].

    min(x)=0 & max(x)=2

    p(x)=1/pi uniformly in [0,pi]. Where p(x) is distribution of probability of variable x.

    x/2=1*sin(alpha/2), alpha=angle between sides of triangle formed by ladybugs and center of circle.

    x=2*sin(alpha/2) & dx = cos(alpha/2)

    E[x]=2*int(0_2){x*p(x))=2*int(0_pi){(1/pi)*sin(alpha)d(alpha)} = 4/pi.

    Note: int(a_b){f(x)} is integral between limits a & b of function f.

    MIGUE.

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