Define the nth moment of the random variable X. Dene the nth central moment
of a random variable X. Finally, dene the moment generating function, M(t).
Write down a few terms of the series expansion of a general M(t). Why is the
series expansion relevant in terms of calculating moments?
solution; from the given data,
nth moment: The nth moment of a random variable X is defined as
nth Central moment: The nth central moment of a random variable X is defined as
Moment generating function: The moment generating function(MGF) M(t) of a random variable X is defined as:
M(t) exist if there exist a positive constant 'a' such that
M(t) is finite for all t € [-a , a].
Expansion of M(t):
we can see in the expansion of mgf coefficients of is the rth moment of random variable X that's why series expansion of MGF is relevant in terms of calculating moments. please give a like, thank you
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