# Escalate - Show every mynute steps in DETAILED!

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Escalate - Show every mynute steps in DETAILED!

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Step 1

Given X is binomial distribution with parameters n,p.
The moment generating funciton of binomial distribution is given below

Step 2

If X is a random variable with with moment generating function MX(t) then
E[Xn] = MXn(0)
where MXn(t) is nth derivative of MX(t).
Deriving the moment generating function three times we get the following
We use the chain rule to derivate the given moment generating function. help_outlineImage TranscriptioncloseMy)=((1-p)+pe (a-p) + pe) - m(a-p) + pe') (pe) M)n(a-p)pe (pe)- mn-(a-p)+ pe ) d 7-1 77 ре dt d (pe п(n dt +(a-p)+pe) (pe) ME)n-(-p) + pe) (pe+n(a-p)+ pe (pe n-1 п(п-1) dt ре ре n-2 7-3 (pe' ) +2(pe'n(n-)(1-p)+pe') =nn-1)-2)(a-p)+ pe) n- 1-2 +(p)+pe) (pe) + m(n- 1)(a-p) + pe)" (pe) fullscreen
Step 3

Derivating the moment generating function for fou... help_outlineImage Transcriptionclosed M )(n-n-2)((1- p)+ pe) (pe' +2(pe )}mn=1)(1-p)+pe') n-3 n-2 dt +n(a-p)+pe' (pe') + mn=1)((1-p)+ pe') (pe = (n(n-1)(1-2)(1-3)(1-p) + pe') (pe)+(nn-1)(1-2)((1-p)+ pe )*° 3( p¢ ) +4(pe') n(n-(p)+ pe')+2(pe'n(n-1)(1-2)((1-p)+ pe') 7-4 1-3 n-2 +n(1-)(a-p)+pe) (pe+n(1-p)+ pe ) (pe' ) +Mn-)01-2)(a-p)+pe) (pe+mn-1)(1-p) + pe) 2(pe) n-1 n-3 fullscreen

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### Probability 