Let X1 X2 Xn Uniform0 1 Find the probability density funct

Let X_1, X_2, ..., X_n ~ Uniform(0, 1). Find the probability density function for V = Y_n - Y_1, where Y_1 = min {X_1, X_2, ..., X_n} and y_n = max {X_1, X_2, X_n}.

the density fuction of iids x1,x2,x3 ,.....Xn is 1 .

there is no minimum and max values unless limits are defined for individual RV s

so Y_n = n and Y₁ = 1

V = n - 1.is the probability density function of V

$Let X_1, X_2, ..., X_n ~ Uniform(0, 1). Find the probability density function for V = Y_n - Y_1, where Y_1 = min {X_1, X_2, ..., X_n} and y_n = max {X_1, X_2,$

Let X1 X2 Xn Uniform0 1 Find the probability density funct

Solution

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