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A die is rolled. If denotes the number of positive divisors of the outcome then the range of the random variable is
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The correct answer is:
The possible outcomes with their positive divisors are:-
\(
\begin{array}{|c|c|c|}
\hline \text { outcome } & \text { positive divisors } & \text { number (X) } \\
\hline 1 & 1 & 1 \\
\hline 2 & 1,2 & 2 \\
\hline 3 & 1,3 & 2 \\
\hline 4 & 1,2,4 & 3 \\
\hline 5 & 1,5 & 2 \\
\hline 6 & 1,2,3,6 \\
\hline
\end{array}
\)
Hence, Range of \(X=\{1,2,3,4\}\)
\(
\begin{array}{|c|c|c|}
\hline \text { outcome } & \text { positive divisors } & \text { number (X) } \\
\hline 1 & 1 & 1 \\
\hline 2 & 1,2 & 2 \\
\hline 3 & 1,3 & 2 \\
\hline 4 & 1,2,4 & 3 \\
\hline 5 & 1,5 & 2 \\
\hline 6 & 1,2,3,6 \\
\hline
\end{array}
\)
Hence, Range of \(X=\{1,2,3,4\}\)
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