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4 moment generating functions moment generating functions (mgf) are a very powerful computational tool In formulas we have ∞ mk(x) They make certain computations much shorter

However, they are only a computational tool The moment generating function m(t) of a random variable x is the exponential generating function of its sequence of moments The mgf has no intrinsic meaning.

Moment generating functions definition 2.3.6

The moment generating function (mgf) of a random variable x is ( åx etxfx(x) if x has a pmf mx(t) = e(etx) = Moment generating functions 13.1 basic facts mgf::overview n the prob de nition Find the moment generating function of p oisson( ) Find the moment generating function of exp( )

Find the moment generating function of n(0 Let x, y be independent random variables with moment generating functions mx(t) Then, the moment generating function of the sum of these two random variables is equal to the product of the individual moment. 3 the moment generating function of a random variable in this section we define the moment generating function m(t) of a random variable and give its key properties

We start with definition 12

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