Question

to exercises 4.141 and 4.137. suppose that y is uniformly distributed on the interval (0, 1) and that a > 0 is a constant. a give the moment-generating function for y. b derive the moment-generating function of w

Answer 1

The moment-generating function for y is given as eⁿᵇ - eⁿᵃ / n(b-a) and derivation of  moment-generating function of y is e-1/t

Given that,

The interval (0, 1) is covered by a uniform distribution of y, and a > 0 is a constant.

The moment generating function is eⁿᵇ - eⁿᵃ / n(b-a)

The given interval is (0,1)

Here a =0;

         b=1;

Now substitute the values of a and b in the above moment generating function we get,

y=eⁿᵇ - eⁿᵃ / n(b-a)

y=e^1-e^0/t(1-0)

y= e-1/t

Therefore, the derivation of the moment generating function is e-1/t

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