A) \[(3,\,1/9)\]
B) \[(\,1/9,3)\]
C) \[(\,1/8,4)\]
D) \[(\,1,3)\]
Correct Answer: B
Solution :
We know sum of probability distribution is 1 \[\therefore \] \[k+2k+3k+2k+k=1\] \[\Rightarrow \] \[9k=1\] \[\Rightarrow \] \[k=\frac{1}{9}\] Mean \[=\underset{i=1}{\mathop{\overset{5}{\mathop{\Sigma }}\,}}\,{{p}_{i}}{{x}_{i}}=k(1)+2k(2)+3k(3)\] \[+2k(4)+k(5)\] \[=k(1+4+9+8+5)\] \[=\frac{1}{9}\times 27=3\] \[\therefore \] \[(k,m)=\left( \frac{1}{9},3 \right)\]
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