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Let X be a random variable with density f X ( x ) = ( 1...

Let X be a random variable with density f X ( x ) = ( 1 / 2 ) cos ⁡ x for x ∈ [ − π / 2 , π / 2 ]. (a) Show that this is a valid density function. (b) What is the distribution function of Y = sin ⁡ X? (c) What is the density function of Y?

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