Let the vector of random variables (X1, X2, X3) have the trinomial pdf with parameters n, p1,
Question:
P(X1 = k1, X2 = k2, X3 = k3) = n!/k1! k2! k3! pk11 pk22 pk33,
ki = 0, 1, . . . , n; i = 1, 2, 3; k1 + k2 + k3 = n
By definition, the moment-generating function for (X1, X2, X3) is given by
MX1, X2, X3 (t1, t2, t3) = E(et1X1+t2 X2+t3 X3)
Show that
MX1,X2,X3 (t1, t2, t3)=(p1et1 + p2et2 + p3et3)n
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Where the summation extends over all the values of k 1 k 2 k 3 s...View the full answer
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Related Book For
Introduction To Mathematical Statistics And Its Applications
ISBN: 9780321693945
5th Edition
Authors: Richard J. Larsen, Morris L. Marx
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