 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/m/m1/b/iii/solution

Let

X_{1}^{'}

be an independent copy of

X_{1}

and take

Y = X_{1} + X_{1}^{'}

. Then

M_{Y} (t) = M_{1} (t)^{2} .

Independence of the copy is essential. The variable

2 X_{1}

M_{1} (2 t)

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