Question: (a) Show that the following are probability density functions (p.d.f.'s): (b) Prove or disprove: If f1 (x) and f2 (x) are p.d.f.?s and if ?

(a) Show that the following are probability density functions (p.d.f.'s):

f(x) = e-*I(0.)(x) f(x) = 2e-2x I(0.)(x) f(x) = (0+ 1)fi(x) O(x) (b) Prove or disprove: If f1 (x) and f2 (x) are p.d.f.?s and if ? ₁ + ? ₂ = 1, then ? ₁f ₁(x) + ? ₂f ₂(x) is a p.d.f.

f(x) = e-*I(0.)(x) f(x) = 2e-2x I(0.)(x) f(x) = (0+ 1)fi(x) O(x) - 0

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