Q1. (3 points) Assume that X ~ Pareto (a) with the density where a 0. f(x)...

 

Transcribed Image Text:

Q1. (3 points) Assume that X ~ Pareto (a) with the density where a 0. f(x) = { | -1 x1 " x <1 , (a) Calculate E[X] and Var[X]. What do you need to assume about a for E[X] and Var[X] to be finite? (b) Find the density of X + b. (c) Find the cumulative distribution function of Y = log X. (d) Find the cumulative distribution function of Y = x. Q1. (3 points) Assume that X ~ Pareto (a) with the density where a 0. f(x) = { | -1 x1 " x <1 , (a) Calculate E[X] and Var[X]. What do you need to assume about a for E[X] and Var[X] to be finite? (b) Find the density of X + b. (c) Find the cumulative distribution function of Y = log X. (d) Find the cumulative distribution function of Y = x.