Let the random variable X have probability density function f(x) = 1 π , − π 2 < x < π 2 . Find the probability density function of Y = sin X by (a) cumulative distribution function technique, (b) transformation technique. Hint: The derivative of x = arcsin y is dx dy = √ 1 1−y 2 .

Either enter an exact answer in terms of \piπ or use 3.143.14 for \piπ and enter your answer as a decimal.

Select the correct answer and solve for y

Match the following reasons with the statements given to create the proof. 1. do = ob, ao = oc sas 2. doc = aob given 3. triangle cod congruent to triangle aob vertical angles are equal. 4. 1 = 2, ab = dc if two sides = and ||, then a parallelogram. 5. ab||dc if alternate interior angles =, then lines parallel. 6. abcd is a parallelogram cpcte