[Solution Library] [2+3+2+3= 10 pts] Let X be a discrete random variables that takes nonnegative integer values, and is associated with a transform of the

Question: [2+3+2+3= 10 pts]

Let X be a discrete random variables that takes nonnegative integer values, and is associated with a transform of the form

\[{{M}_{X}}\left( s \right)=c\frac{1+2{{e}^{3s}}}{3-{{e}^{s}}}\]

where c is some constant. Find (a) ${{p}_{X}}\left( 3 \right)$ (b) E(X) (c) ${{p}_{X}}\left( 1 \right)$ and (d) $E\left( X|X\ne 0 \right)$.

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[Solution Library] [2+3+2+3= 10 pts] Let X be a discrete random variables that takes nonnegative integer values, and is associated with a transform of the

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