Let X be a discrete random variable with the following density function: fx(n) = Sce-2: 2n...

 

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Let X be a discrete random variable with the following density function: fx(n) = Sce-2: 2n n! n O c3n n < 0 Define the variables U, V as follows: (-X U = 0 X < 0 X 0 V = = {x X < 0 X O (Four Parts) a) Define W = U + V and W = U-V. What is Cov(W, W2)? (Hint: solve for constant c first, and then find random variables U,V,W) Let I be a bernoulli random variables that takes value 1 with probability 0.7. Assume T is independent of both U, V. b) (13 points) What is E(U T +V (1 T))? Let V1, V2, V3, , ... be a sequence of independent and identically distributed random variables each having the same distribution as V. c) (14 points) Use the central limit theorem to approximately find P(20 Let X be a discrete random variable with the following density function: fx(n) = Sce-2: 2n n! n O c3n n < 0 Define the variables U, V as follows: (-X U = 0 X < 0 X 0 V = = {x X < 0 X O (Four Parts) a) Define W = U + V and W = U-V. What is Cov(W, W2)? (Hint: solve for constant c first, and then find random variables U,V,W) Let I be a bernoulli random variables that takes value 1 with probability 0.7. Assume T is independent of both U, V. b) (13 points) What is E(U T +V (1 T))? Let V1, V2, V3, , ... be a sequence of independent and identically distributed random variables each having the same distribution as V. c) (14 points) Use the central limit theorem to approximately find P(20