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Problem The probability density function of a random variable Y Y Y g ( y ) = { 4 π 4 + π sin ( π y ) for 0 ≤ y < 1 2 4 π 4 + π ( 2 − 2 y ) for 1 2 ≤ y ≤ 1 0 otherwise g(y) = \begin{cases} \frac{4\pi}{4 + \pi} \sin(\pi y) & \text{for } 0 \le y < \frac{1}{2} \\ \frac{4\pi}{4 + \pi} (2 - 2y) & \text{for } \frac{1}{2} \le y \le 1 \\ 0 & \text{otherwise} \end{cases} g ( y ) = ⎩ ⎨ ⎧ 4 + π 4 π sin ( π y ) 4 + π 4 π ( 2 − 2 y ) 0 for 0 ≤ y < 2 1 for 2 1 ≤ y ≤ 1 otherwise P ( 1 4 < Y ≤ 3 4 ) P\left(\frac{1}{4} < Y \le \frac{3}{4}\right) P ( 4 1 < Y ≤ 4 3 ) Browse the problem library