Use integration to derive the moment-generating function MX (t) where fX (x) = (1/3) e^(−x/3) for x > 0. (Since we ar...

Question

Question

Use integration to derive the moment-generating function MX (t) where fX (x) = (1/3) e^(−x/3)

for x > 0. (Since we are maily interested in t near 0, assume that t < 1/3 .) Then use MX (t)

to compute E(X), E(X^2), V (X), and E(X^3).

Answer 1

Answer #1

8. Fx (x) = { 0312x30 My(t) = E(etx) = pt 4 x = 1 EL-13) * - * [ 31 31 (0-1) = [-3E Macta de leite 1-35)2 M(O)=3 M(t): ce su

Answer 2

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