2. Let X and Y be independent random variables with common distribution function F and density function f. Show that V = max(X, Y) has distribution function P(V ≤ x) = F(x)2 and density function fy(x) = 2 f(x)F(x), x € R. Find the density function of U = min{X, Y}.

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Q: a) Check whether X and Y are independent

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A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

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Q: a) Find marginal density functions. Are Y1 and Y, independent? b) Find P(0 < Y < 0.3, –2 < Y2 < 1).…

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Q: i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).

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Q: Find the density of X = max(Y1,Y2), where Y1 and Y2 are independent random variables with densities…

A: It is an important part of statistics . It is widely used .

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A: It is an important part of statistics. It is widely used.

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