Question: Let (X1, X2) [0, 1] [0, 1] be a random sample from a probability distribution with probability density function f(x) = 3x x =

Let (X1, X2) [0, 1] [0, 1] be a random sample from

Let (X1, X2) [0, 1] [0, 1] be a random sample from a probability distribution with probability density function f(x) = 3x x = [0,1] 10 otherwise Let g(y1, y2) be the joint distribution of the vector of order statistics Y = (X(1), X(2)). < Find the probability P(X (1) X(2)). Round to three decimals. Type your answer... 5 points Consider the previous problem. What is the probability. P(X (2) X (1))? Round to three decimals. Type your answer... 5 points Let (X1,...,xn) be a random sample from the Unif(0, 1) distribution. Find the probability P(X (1) .1) when n = 20. Round to three decimals. Type your answer... 5 points Consider the previous problem. Find the probability P(X (n) .9) when n = 20. Round to three decimals.

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