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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
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If mean of $X$ is 4.2 , then $a$ and $b$ are respectively equal to
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Verified Answer
The correct answer is:
$0.1,0.2$
$$
\text { We have }
$$
$$
\begin{array}{rlrl}
\Sigma P_j & =a+a+a+b+b+0.3 \\
\Rightarrow & 1 & =3 a+2 b+0.3 \\
\Rightarrow & 3 a+2 b & =0.7 \\
& \sum P_j x_j & =a+2 a+3 a+4 b+5 b+1.8 \\
\Rightarrow & 4.2 & =6 a+9 b+1.8 \\
\Rightarrow & 2 a+3 b & =0.8
\end{array}
$$
Solving Eqs. (i) and (ii), we get
$$
a=0.1, b=0.2
$$
\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
$$
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