According to quantum mechanics, the x x - and y y -coordinates of a particle confined to

According to quantum mechanics, the $x$ - and $y$-coordinates of a particle confined to the region $R=$ $[0,1]\times [0,1]$ are random variables with joint probability density function

$$p(x,y)=\{\begin{array}{cc}C{\sin }^2\left(2\pi \ell x\right){\sin }^2\left(2\pi ny\right)& \text{if}(x,y)\in R\\ 0& \text{otherwise}\end{array}$$

The integers $\ell$ and $n$ determine the energy of the particle, and $C$ is a constant.

(a) Find the constant $C$.

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(b) Calculate the probability that a particle with = 2, n = 3 lies in the region [0, 1] [0, }].