11. Tilted distributions. (a) Let X have distribution function F and let T be such that M(T) = E(e¹x) < <∞o. Show that F(x) = M(t)-¹ Sety dF (y) is a distribution function, called a 'tilted distribution' of X, and find its moment generating function. (b) Suppose X and Y are independent and E(et X), E(e¹Y)<∞o. Find the moment generating function of the tilted distribution of X + Y in terms of those of X and Y.

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