Question: A random variable is generated as follows. We flip a coin. With probability, the result is Heads, and thenis generated according to a PDF| which

A random variable is generated as follows. We flip a coin. With probability, the result is Heads, and thenis generated according to a PDF| which is uniform on[0,1].

With probability1 the result is Tails, and then is generated according to a PDF| of the form |

()=2,if[0,1].

(The PDF is zero everywhere else.)

What is the (unconditional) PDF()of?

For01

()=

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