Statistics-And-Probability Question 646
Question: The range of a random variable x is $ {1,2,3,…}. $ If $ P(x=r)=\frac{1}{2^{r}} $ , then the mean of the distribution is
Options:
A) 8
B) 16
C) 1
D) 2
Show Answer
Answer:
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 $
BETA
