34.- Let X1,., Xn a random sample of the population with distribution Beta(a, 2), a > 0, ß = 2, whose density function is Г(а+ 2) ª-'(1 – x)', T'(a)I'(2) f(x; a) 0 < x <∞ zero in any other case. Show that S(X) = X1X2· ·· Xn = II"1 X; (the product) is %3D a sufficient statistic for a.

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34.-

34.- Let X1,., Xn a random sample of the population with distribution Beta(@, 2),
a > 0, B = 2, whose density function is
Г(а + 2)
I'(@)I(2)'
(1 – x)',
f(x; a)
0 < x < ∞
zero in any other case. Show that S(X) = X1X2…X, = II", X; (the product) is
a sufficient statistic for a.
Transcribed Image Text:34.- Let X1,., Xn a random sample of the population with distribution Beta(@, 2), a > 0, B = 2, whose density function is Г(а + 2) I'(@)I(2)' (1 – x)', f(x; a) 0 < x < ∞ zero in any other case. Show that S(X) = X1X2…X, = II", X; (the product) is a sufficient statistic for a.
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