Suppose X₁, X2, ···, XN are drawn iid from a distribution with the following probability density function (pdf): f_{\alpha}(x)=\left\{\begin{array}{ll} C x^{\alpha} & \text { for } x \in[0,1] \\ 0 & \text { otherwise } \end{array}\right. where a > 0 is an unknown parameter.(a) (2 points) What should be the value of C in order for få to be a valid pdf? (b) (4 points) What is the expected value of X₁? State your answer in terms of a. (c) (4 points) You collect N = 100 data points with sample mean = 0.84. Using the method-of-moments approach, provide an estimate for a.

Solved: Suppose X₁, X2, ···, XN are drawn iid from a distribution with the fo

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suppose x x2 xn are drawn iid from a distribution with the following p

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Suppose X₁, X2, ···, XN are drawn iid from a distribution with the following probability density function (pdf): f_{\alpha}(x)=\left\{\begin{array}{ll} C x^{\alpha} & \text { for } x \in[0,1] \\ 0 & \text { otherwise } \end{array}\right. where a > 0 is an unknown parameter.(a) (2 points) What should be the value of C