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Math · Statistics And Probability
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3. Let Y1, Y2, . .., Yn denote a random sample from the probability density function 0くyく1; θ>0 f(y | θ)--@ye-1 , 0, elsewhere. (a) Show that this density function is in the exponential family and that Σ=1-ln(X) is sufficient for θ. (b) If WiIn(Yi), show that Wi has an exponential distribution with mean 1/6e. (c) Show that 2θΣ 1 W, has a X2 distribution with 2n degrees of freedom. (d) Show that

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