ZeroScope
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The ’moments’ <t**n> of the distribution p(t) are defined as:
<t**n> = integral from (0, infinity) p(t).t**n dt (1) where ** denotes to the power of
Show (analytically) that
<t**n> = n!τ**n (2)
Hint: Use integration by parts to show that
<t**n> = nτ<t**n-1> (3)
and use mathematical induction
I have solved the integral to get equation 3 but i can't begin to think on where to start the mathematical induction. Its been so long since i have done it.
At first i thought that doing <tn>.<tn-1> = blabla would work but i get the answer
blabla = nτ<t**n-1> . (n-1)τ<t**n-2>
but i really think I am missing the mark by a lot.
Sorry about the bad formatting.
<t**n> = integral from (0, infinity) p(t).t**n dt (1) where ** denotes to the power of
Show (analytically) that
<t**n> = n!τ**n (2)
Hint: Use integration by parts to show that
<t**n> = nτ<t**n-1> (3)
and use mathematical induction
I have solved the integral to get equation 3 but i can't begin to think on where to start the mathematical induction. Its been so long since i have done it.
At first i thought that doing <tn>.<tn-1> = blabla would work but i get the answer
blabla = nτ<t**n-1> . (n-1)τ<t**n-2>
but i really think I am missing the mark by a lot.
Sorry about the bad formatting.