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Find the M.G.F. of Poisson Distribution.

Hence find its variance and mean.

1 Answer
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Solution:

i) Moment Generating Function (M.G.F.)

The M.G.F. about the origin is:

M0(t)=E(etx)=p(x)etx=x=0emmxx!.etx=emx=0(met)xx!=em.emet

M0(t)=em(et1)

ii) Mean and Variance of Poisson Distribution

μ1=E(x)=pixi=x=0emmxx!x=x=1emmx(x1)!=memx=1m(x1)(x1)!

μ1=mem[1+m+m22!+m33!+]=mem.em=m

Mean =μ1=m

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