Question: Picture attached, Please solve step by step! Thanks! a) Prove that fx(x) 2 0 for all x E R. Hint you can use that derivative

Picture attached, Please solve step by step! Thanks! a) Prove that fx(x) 2 0 for all x E R. Hint you can use

Picture attached, Please solve step by step! Thanks!

a) Prove that fx(x) 2 0 for all x E R. Hint you can use that derivative function g is not negative in between [a,b], but and only if min . xE[a,big (x) 2 0 b) Prove that f fx(x)dx = 1 c) Draw function fx graph between [-2,2.5], explain what does it mean that f_ fx(x)dx = 1. d) Determine the expected value of a random variable related to the density function fX(x).

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