GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/23

Question 23 (Textile Engineering & Fibre Science)

The distribution function $P_X(k)$ of a random variable $X$ with parameter $\lambda$ , satisfies the relation $P_X(k+1)=\frac{\lambda}{k+1}P_X(k)$ , $k=0,1,2,3 ......$ .
If $P_X(0)=e^{-\lambda}$ , the expression obtained for $P_X(k)$ from above relation is

P_X(k)=\frac{\lambda^{k+1}}{(k+1)!}e^{\lambda}

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GATE Textile Engineering and Fibre Science (TF) Question Papers | GATE Textile Question Answer | GATE Textile Solved Question Papers | GATE Textile Papers | GATE Textile Answer Key

(A)	$P_X(k)=\frac{\lambda^k}{k!}e^{\lambda}$
(B)	$P_X(k)=\frac{\lambda^{k+1}}{(k+1)!}e^{\lambda}$
(C)	$P_X(k)=\frac{\lambda^k}{k!}e^{-\lambda}$
(D)	$P_X(k)=\frac{\lambda^{k+1}}{(k+1)!}e^{-\lambda}$