2. Show wheth er each of the following satisfy the conditions to be a probability density:...

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2. Show wheth

er each of the following satisfy the conditions to be a probability density:

⎪⎨

0 x < 0

(a) f(x) = ⎪x 0 ≤ x ≤ 2

0 x > 2 1/2 −1 < x < 1

(b) f(x) =

0 otherwise 2x 1 < x < 2

(c) f(x) = 3 −

0 otherwise e−x x > 0

(d) f(x) = 0 otherwise

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