The probability density function of a random variable is given by g(y) = cases 4 4 +…

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Statistics and Probability · Statistics and Probability

Problem

The probability density function of a random variable

Y

is given by

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}

Find

P\left(\frac{1}{4} < Y \le \frac{3}{4}\right)