Question: Let a r.v. X have the density (a) Explain why P(X / [0,2])= 0. Without any calculations, find P(0 X 1) and P(1

Let a r.v. X have the densityLet a r.v. X have the density(a) Explain why P(X /∈ [0,2])=

(a) Explain why P(X /∈ [0,2])= 0. Without any calculations, find P(0 ≤ X ≤ 1) and P(1 ≤ X ≤ 2).

(b) Reasoning heuristically, explain why E{X} should be equal to0. Without any calculations, find P(0 ≤ X ≤ 1) and P(1

Calculate E{X} rigorously.

(c) State and answer similar questions for the case≤ X ≤ 2).(b) Reasoning heuristically, explain why E{X} should be equal

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