- #1

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Problem:

X is a continuous random variable with a proabaility density function:

f(x) = 1/4 if -2<=x<=2

0 other wise

Let Y=1/X. Then P(Y<=1/2) = ?

This is how I approached the problem:

P(Y<=1/2)=P(1/x=1/2)

=P(X>=2)

Taking the intergral of f(x) with limits of integration -2,2.

My answer is 1.

However the answer given is 1/2.

Any ideas.