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(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):

(b) Prove or disprove: If f1 (x) and f2 (x) are p.d.f.?s and if ? 1 + ? 2 = 1, then ? 1 f 1 (x) + ? 2 f 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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