6.1 6.2 Let y be a random variable with probability density function given by 0 y...

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6.1 6.2 Let y be a random variable with probability density function given by 0≤ y ≤ 1, = {20¹ elsewhere. a b f(y) = Find the density function of U₁ = 2Y - 1. Find the density function of U₂ = 1-2Y. C Find the density function of U3 = Y². d Find E(U₁), E(U₂), and E(U3) by using the derived density functions for these random variables. Find E(U₁), E (U₂), and E(U3) by the methods of Chapter 4. Let Y be a random variable with a density function given by (3/2) y², -1≤ y ≤ 1, elsewhere. e 2(1-y), f(y) = -{(3/2)y², 0, a Find the density function of U₁ = 3Y. b Find the density function of U₂ = 3 - Y. C Find the density function of U3 = y². 6.1 6.2 Let y be a random variable with probability density function given by 0≤ y ≤ 1, = {20¹ elsewhere. a b f(y) = Find the density function of U₁ = 2Y - 1. Find the density function of U₂ = 1-2Y. C Find the density function of U3 = Y². d Find E(U₁), E(U₂), and E(U3) by using the derived density functions for these random variables. Find E(U₁), E (U₂), and E(U3) by the methods of Chapter 4. Let Y be a random variable with a density function given by (3/2) y², -1≤ y ≤ 1, elsewhere. e 2(1-y), f(y) = -{(3/2)y², 0, a Find the density function of U₁ = 3Y. b Find the density function of U₂ = 3 - Y. C Find the density function of U3 = y².