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2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y

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Facts 1) Let fy(y), Fy(y)(- P(Y s y)) be the pdf and cdf (cumulative distribution function) of the random variable Y respecti0; otherwise Now we have to find pdf of y = sin (X) Consider F1(y)=P(YS) = P(sin (X) y) = P (X sin-1(y)) sin(y) sin-1(y) dx 06(y)-2 * Fir(v)-2 * (sin-1(y))-2 (sin-1 (y)) (v from fact 1) dy d (2 d, (sin-10)) 2 (sin-1(y) ) * 2 1 0; otherwise

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