(Solved): Suppose the following data are a random sample from a distribution with probability density func ...

Suppose the following data are a random sample from a distribution with probability density function given by BxB-1 f(x|3) 0 < x < 25, p > 0. 258 20.9 21.7 23.1 23.5 22 22.8 23.8 23.8 23 23 23.9 24 23.1 25 Some summary statistics: 214, Xi 323.60 and 214, in(xi) = 43.9527 = (a) Estimate ß using the method of moments. a Using Method of Moments We Compute the ist Moment. 25 ] E [a] = Safe ) Bx.no de tx 25B 0 25 25 j b 3+1 doc - 3x 296 b 0 (B+1) 25 o - 25 251 b 8+) (B+1) 25 25 l = -XB + X 25 2 - X b = = x => 3 [as-p] = x EX n B = X as- {x as- n 323-60/14 = a5 323 60/14 = verir 7 12.2576 (d) Use the asymptotic normality property of MLEs to construct the 95% approx- imate confidence interval for B. (2)