Question: Let X1, ...,X5 be a random sample from the BETA(2, 1) distribution. (i) Find the density of a joint distribution of X1:5,X2:5,X4:5. (ii) Obtain E(X2:5|X4:5).

Let X1, ...,X5 be a random sample from the BETA(2, 1) distribution. (i) Find the density of a joint distribution of X1:5,X2:5,X4:5. (ii) Obtain E(X2:5|X4:5).

(iii) Obtain E(X4:5|X2:5). (iv) Find the distribution of Y = X2:5/X1:5. (v) Check if variables X1:n/Xn:n and Xn:n are independent.

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