Q75 / 160 · TS EAMCET 2017 · Mathematics
The probability distribution of a random variable $X$ is given below
If mean of $X$ is 4.2 , then $a$ and $b$ are respectively equal to
If mean of $X$ is 4.2 , then $a$ and $b$ are respectively equal to
- A$0.3,0.2$
- B$0.1,0.4$
- Correct answerC$0.1,0.2$
- D$0.2,0.1$
Solution
$$
\text { We have }
$$
$$ \begin{array}{rlrl} \Sigma P_j & =a+a+a+b+b+0.3 \\ \Rightarrow & 1 & =3 a+2 b+0.3 \\ \Rightarrow & 3 a+2 b & =0.7 \\ & \sum P_j x_j & =a+2 a+3 a+4 b+5 b+1.8 \\ \Rightarrow & 4.2 & =6 a+9 b+1.8 \\ \Rightarrow & 2 a+3 b & =0.8 \end{array} $$ Solving Eqs. (i) and (ii), we get $$ a=0.1, b=0.2 $$
$$ \begin{array}{rlrl} \Sigma P_j & =a+a+a+b+b+0.3 \\ \Rightarrow & 1 & =3 a+2 b+0.3 \\ \Rightarrow & 3 a+2 b & =0.7 \\ & \sum P_j x_j & =a+2 a+3 a+4 b+5 b+1.8 \\ \Rightarrow & 4.2 & =6 a+9 b+1.8 \\ \Rightarrow & 2 a+3 b & =0.8 \end{array} $$ Solving Eqs. (i) and (ii), we get $$ a=0.1, b=0.2 $$
Hence, the correct answer is option: 'C'.