Question: Find a constant (C) such that [p(x, y)= begin{cases}C y & text { if } 0 leq x leq 1 text { and } x^{2}

Find a constant \(C\) such that

\[p(x, y)= \begin{cases}C y & \text { if } 0 \leq x \leq 1 \text { and } x^{2} \leq y \leq x \\ 0 & \text { otherwise }\end{cases}\]

is a joint probability density function. Then calculate the probability that \(Y \geq X^{3 / 2}\).

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