44.2 Suppose $Y_1, \dots, Y_n$ are a random sample from the density \\ $f_\theta(y; \theta) = \frac{3y^2}{\theta^3}$ for $0 < y < \theta$. \\ Find the method of moments estimator for $\theta$.
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Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ be a random sample from the probability density function given by $$f(y | \theta)=\left\{\begin{array}{ll} \frac{\Gamma(2 \theta)}{[\Gamma(\theta)]^{2}}\left(y^{\theta-1}\right)(1-y)^{\theta-1}, & 0 \leq y \leq 1 \\ 0, & \text { elsewhere } \end{array}\right.$$Find the method-of-moments estimator for $\theta$
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