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The probability distribution of a discrete random variable $\mathrm{X}$ is
Find the value of $\mathrm{P}(2 < \mathrm{X} < 6)$
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Find the value of $\mathrm{P}(2 < \mathrm{X} < 6)$
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Verified Answer
The correct answer is:
$\frac{4}{7}$
We have $\mathrm{K}+2 \mathrm{~K}+3 \mathrm{~K}+4 \mathrm{~K}+5 \mathrm{~K}+6 \mathrm{~K}=1 \Rightarrow \mathrm{K}=\frac{1}{21}$
$$
\begin{aligned}
& \therefore \mathrm{P}(2 < \mathrm{x} < 6)=\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4)+\mathrm{P}(\mathrm{x}=5) \\
& =\frac{3}{21}+\frac{4}{21}+\frac{5}{21}=\frac{12}{21}=\frac{4}{7}
\end{aligned}
$$
$$
\begin{aligned}
& \therefore \mathrm{P}(2 < \mathrm{x} < 6)=\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4)+\mathrm{P}(\mathrm{x}=5) \\
& =\frac{3}{21}+\frac{4}{21}+\frac{5}{21}=\frac{12}{21}=\frac{4}{7}
\end{aligned}
$$
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