A) 8
B) 16
C) 1
D) 2
Correct Answer: D
Solution :
[d] Mean \[E(x)=\Sigma rP(r)=\Sigma r.\frac{1}{{{2}^{r}}}\] \[\therefore E(x)=\frac{1}{2}+\frac{2}{{{2}^{2}}}+\frac{3}{{{2}^{3}}}+...\] \[\frac{1}{2}E(x)=\frac{1}{{{2}^{2}}}+\frac{2}{{{2}^{3}}}+...\] \[\therefore \frac{1}{2}E(x)=\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{2}^{3}}}+...=\frac{1/2}{1-1/2}\] \[\therefore E(x)=2\]
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