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Q48Section C (Section C)48 of 60

MOM estimate of a Beta shape

Let X1,X2,X3,X4X_{1},X_{2},X_{3},X_{4} be a random sample of size 44 from a distribution with the probability density function f(x)={α(α+1)xα−1(1−x),0<x<1,0,otherwise,f(x)=\begin{cases}\alpha(\alpha+1)x^{\alpha-1}(1-x),&0<x<1,\\0,&\text{otherwise,}\end{cases} where α>0\alpha>0 is an unknown parameter. Based on the observed data 0.2,0.1,0.3,0.40.2,0.1,0.3,0.4, the method of moments estimate of α\alpha equals __________ (rounded off to two decimal places)

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