Let X be a uniform random variable over (0,1). Let a and b be two positive...

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Let X be a uniform random variable over (0,1). Let a and b be two positive...

Let X be a uniform random variable over (0,1). Let a and b be two positive numbers and let Y = aX+b.

(a) Determine the moment generating function of X.

(b) Determine the moment generating function of Y.

(c) Using the moment generating function of Y, show that Y is uniformly distributed over an interval(a, a+b).

math Statistics-And-Probability

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Answer 1

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Let X be a unirorro) random variable over CO,1) OLX omgros * Is, MxC etx & Conds letx dx etx I M*(+) : ét-II ,+0 t blet Y= ax ich is same as mgf Of Uniform dists 2. Yn Uniform (bea+b)

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